• Number of free polyominoes (or square animals) with n cells.

    From henhanna@gmail.com@21:1/5 to All on Sat Oct 29 18:54:58 2022
    we're (were) counting rotation, reflection as Separate Animals.
    so our seq. went:
    1, 2, 6, 19, ..............

    ---------- is this seq. not in oeis ?


    (we say 19, the following list says 5)




    https://oeis.org/A000105

    A000105 Number of free polyominoes (or square animals) with n cells. (Formerly M1425 N0561)

    1, 1, 1, 2, 5, 12, 35, 108, 369, 1285, 4655, 17073, 63600, 238591, 901971, 3426576, 13079255, 50107909, 192622052, 742624232, 2870671950, 11123060678, 43191857688, 168047007728, 654999700403, 2557227044764, 9999088822075,
    39153010938487, 153511100594603


    ( starts with 0-cell animal )

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    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Edward Murphy@21:1/5 to henh...@gmail.com on Sat Oct 29 20:23:56 2022
    On 10/29/2022 6:54 PM, henh...@gmail.com wrote:

    we're (were) counting rotation, reflection as Separate Animals.
    so our seq. went:
    1, 2, 6, 19, ..............

    ---------- is this seq. not in oeis ?


    (we say 19, the following list says 5)




    https://oeis.org/A000105

    A000105 Number of free polyominoes (or square animals) with n cells.
    (Formerly M1425 N0561)

    1, 1, 1, 2, 5, 12, 35, 108, 369, 1285, 4655, 17073, 63600, 238591, 901971, 3426576, 13079255, 50107909, 192622052, 742624232, 2870671950, 11123060678, 43191857688, 168047007728, 654999700403, 2557227044764, 9999088822075,
    39153010938487, 153511100594603


    ( starts with 0-cell animal )

    https://oeis.org/A001168

    A001168 Number of fixed polyominoes with n cells.
    (Formerly M1639 N0641) 52
    1, 1, 2, 6, 19, 63, 216, 760, 2725, 9910, 36446, 135268, 505861, 1903890, 7204874, 27394666, 104592937, 400795844, 1540820542,
    5940738676, 22964779660, 88983512783, 345532572678, 1344372335524, 5239988770268, 20457802016011, 79992676367108, 313224032098244, 1228088671826973

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  • From henhanna@gmail.com@21:1/5 to Edward Murphy on Sat Oct 29 20:29:52 2022
    On Saturday, October 29, 2022 at 8:23:59 PM UTC-7, Edward Murphy wrote:
    On 10/29/2022 6:54 PM, henh...@gmail.com wrote:

    we're (were) counting rotation, reflection as Separate Animals.
    so our seq. went:
    1, 2, 6, 19, ..............

    ---------- is this seq. not in oeis ?


    (we say 19, the following list says 5)




    https://oeis.org/A000105

    A000105 Number of free polyominoes (or square animals) with n cells. (Formerly M1425 N0561)

    1, 1, 1, 2, 5, 12, 35, 108, 369, 1285, 4655, 17073, 63600, 238591, 901971, 3426576, 13079255, 50107909, 192622052, 742624232, 2870671950, 11123060678, 43191857688, 168047007728, 654999700403, 2557227044764, 9999088822075, 39153010938487,
    153511100594603


    ( starts with 0-cell animal )


    https://oeis.org/A001168

    A001168 Number of fixed polyominoes with n cells.
    (Formerly M1639 N0641) 52
    1, 1, 2, 6, 19, 63, 216, 760, 2725, 9910, 36446, 135268, 505861,
    1903890, 7204874, 27394666, 104592937, 400795844, 1540820542,
    5940738676, 22964779660, 88983512783, 345532572678, 1344372335524, 5239988770268, 20457802016011, 79992676367108, 313224032098244, 1228088671826973



    thank you... i think there are 2 more variations (in between)

    --- allows rotation only

    --- allows reflection only



    M.Gardner's [The Colosal Book of Math.] has some stuff on Pentominoes (3-D)

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  • From henhanna@gmail.com@21:1/5 to henh...@gmail.com on Tue Nov 1 11:55:54 2022
    On Saturday, October 29, 2022 at 8:29:53 PM UTC-7, henh...@gmail.com wrote:
    On Saturday, October 29, 2022 at 8:23:59 PM UTC-7, Edward Murphy wrote:
    On 10/29/2022 6:54 PM, henh...@gmail.com wrote:

    we're (were) counting rotation, reflection as Separate Animals.
    so our seq. went:
    1, 2, 6, 19, ..............

    ---------- is this seq. not in oeis ?


    (we say 19, the following list says 5)




    https://oeis.org/A000105

    A000105 Number of free polyominoes (or square animals) with n cells. (Formerly M1425 N0561)

    1, 1, 1, 2, 5, 12, 35, 108, 369, 1285, 4655, 17073, 63600, 238591, 901971, 3426576, 13079255, 50107909, 192622052, 742624232, 2870671950, 11123060678, 43191857688, 168047007728, 654999700403, 2557227044764, 9999088822075, 39153010938487,
    153511100594603


    ( starts with 0-cell animal )


    https://oeis.org/A001168

    A001168 Number of fixed polyominoes with n cells.
    (Formerly M1639 N0641) 52
    1, 1, 2, 6, 19, 63, 216, 760, 2725, 9910, 36446, 135268, 505861,
    1903890, 7204874, 27394666, 104592937, 400795844, 1540820542,
    5940738676, 22964779660, 88983512783, 345532572678, 1344372335524, 5239988770268, 20457802016011, 79992676367108, 313224032098244, 1228088671826973
    thank you... i think there are 2 more variations (in between)

    --- allows rotation only

    --- allows reflection only



    M.Gardner's [The Colossal Book of Math.] has some stuff on Pentominoes (3-D)




    i think there are (at least) 2 more variations (in between 5 and 19 shapes)

    --- allows Rotation only ------------------------------ 7 shapes

    --- allows Horizontal Reflection only --------------------- 12 shapes

    are these not in oeis ?

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