A246521 -id:A246521 - cp's OEIS frontend

A367676 a(n) is the denominator of the probability that a particular one of the A335573(n+1) fixed polyominoes corresponding to the free polyomino with binary code A246521(n+1) appears in the version of the Eden growth model described in A367671 when n square cells have been added.

1, 2, 6, 6, 112, 21, 336, 21, 24, 8064, 504, 84, 2520, 40320, 1008, 504, 8064, 8064, 504, 672, 120, 399168, 39916800, 1155, 30240, 18144, 528, 241920, 26880, 36288, 4435200, 1814400, 480, 181440, 480, 2217600, 3991680, 528, 20736, 36288, 362880, 378, 110880, 4435200, 36960, 201600, 5040, 13860, 295680, 5702400, 4435200, 13860, 103680, 50400, 1814400, 720

Offset: 1

Pontus von Brömssen, Nov 26 2023

Can be read as an irregular triangle, whose n-th row contains A000105(n) terms, n >= 1.

Terms on the n-th row are (2*n-1)-smooth.

			As an irregular triangle:
     1;
     2;
     6,   6;
   112,  21, 336,   21,    24;
  8064, 504,  84, 2520, 40320, 1008, 504, 8064, 8064, 504, 672, 120;
  ...

Index entries for sequences related to polyominoes.

Cf. A000105, A246521, A335573, A367671, A367672, A367675 (numerators), A367678, A367765.

A367675(n)/a(n) = (A367671(n)/A367672(n))/A335573(n+1).

A367761 a(n) is the denominator of the probability that the free polyomino with binary code A246521(n+1) appears in the Eden growth model on the square lattice, when n square cells have been added.

Original entry on oeis.org

1, 1, 3, 3, 3, 6, 4, 6, 12, 5, 30, 30, 15, 60, 15, 30, 120, 60, 30, 40, 60, 450, 600, 90, 90, 600, 90, 900, 48, 600, 48, 1800, 90, 450, 90, 40, 48, 90, 1800, 80, 48, 180, 90, 48, 90, 80, 180, 180, 96, 40, 48, 180, 40, 480, 360, 360, 151200, 756000, 756000, 10080, 10080, 151200, 151200, 630, 10080

Offset: 1

Pontus von Brömssen, Dec 02 2023

Can be read as an irregular triangle, whose n-th row contains A000105(n) terms, n >= 1.

			As an irregular triangle:
  1;
  1;
  3,  3;
  3,  6,  4,  6, 12;
  5, 30, 30, 15, 60, 15, 30, 120, 60, 30, 40, 60;
  ...

Index entries for sequences related to polyominoes.

Cf. A000105, A246521, A335573, A367672, A367760 (numerators), A367763, A367764, A367765.

A367760(n)/a(n) = (A367764(n)/A367765(n))*A335573(n+1).

A367764 a(n) is the numerator of the probability that a particular one of the A335573(n+1) fixed polyominoes corresponding to the free polyomino with binary code A246521(n+1) appears in the Eden growth model on the square lattice (see A367760), when n square cells have been added.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 7, 7, 1, 1, 1, 23, 49, 1, 1, 53, 1, 107, 1, 49, 1, 107, 1, 23, 1, 1, 1, 1, 137, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 7, 1, 2797, 70037, 70037, 31, 31, 2797, 3517, 1, 41, 653, 49541, 1, 3517, 71, 67, 41, 899, 2797, 653, 1, 1, 1, 1, 653, 1, 1

Offset: 1

Pontus von Brömssen, Dec 02 2023

Apparently, the probabilities a(n)/A367765(n) are given in Eden (1958) for polyominoes up to 8 cells.

Can be read as an irregular triangle, whose n-th row contains A000105(n) terms, n >= 1.

			As an irregular triangle:
  1;
  1;
  1, 1;
  1, 1, 1, 1, 1;
  1, 1, 1, 1, 7, 1, 1, 7, 7, 1, 1, 1;
  ...

Murray Eden, A probabilistic model for morphogenesis, in: Symposium on Information Theory in Biology (Gatlinburg 1956), pp. 359-370, Pergamon Press, New York, 1958.

Murray Eden, A two-dimensional growth process, in: 4th Berkeley Symposium on Mathematical Statistics and Probability (Berkeley 1960), vol. 4, pp. 223-239, University of California Press, Berkeley, 1961.
Index entries for sequences related to polyominoes.

Cf. A000105, A246521, A335573, A367675, A367760, A367761, A367765 (denominators), A367766.

a(n)/A367765(n) = (A367760(n)/A367761(n))/A335573(n+1).

A367765 a(n) is the denominator of the probability that a particular one of the A335573(n+1) fixed polyominoes corresponding to the free polyomino with binary code A246521(n+1) appears in the Eden growth model on the square lattice (see A367760), when n square cells have been added.

Original entry on oeis.org

1, 2, 6, 6, 24, 6, 16, 24, 24, 20, 120, 120, 120, 480, 120, 120, 480, 480, 120, 40, 120, 1800, 4800, 720, 720, 1200, 720, 7200, 384, 4800, 384, 7200, 720, 1800, 720, 320, 384, 720, 7200, 320, 384, 720, 720, 384, 720, 320, 720, 720, 384, 320, 384, 720, 320, 1920, 1440, 720

Offset: 1

Pontus von Brömssen, Dec 02 2023

Can be read as an irregular triangle, whose n-th row contains A000105(n) terms, n >= 1.

			As an irregular triangle:
   1;
   2;
   6,   6;
  24,   6,  16,  24,  24;
  20, 120, 120, 120, 480, 120, 120, 480, 480, 120, 40, 120;
  ...

Index entries for sequences related to polyominoes.

Cf. A000105, A246521, A335573, A367676, A367760, A367761, A367764 (numerators), A367767.

A367764(n)/a(n) = (A367760(n)/A367761(n))/A335573(n+1).

A368000 a(n) is the numerator of the probability that a particular one of the A335573(n+1) fixed polyominoes corresponding to the free polyomino with binary code A246521(n+1) appears as the image of a simple random walk on the square lattice.

Original entry on oeis.org

1, 1, 1, 1, 1, 4, 1, 1, 1, 97, 1, 1, 1, 8, 1, 1, 8, 8, 1, 1, 1, 867, 9565, 1, 1, 2495, 1, 262781, 389, 9565, 389, 262781, 1, 867, 1, 597, 389, 1, 631381, 597, 389, 1, 1, 389, 1, 597, 1, 1, 389, 597, 389, 1, 597, 2501, 412, 1, 2635, 1706571966622, 1706571966622, 1117, 1117

Offset: 1

Pontus von Brömssen, Dec 09 2023

In a simple random walk on the square lattice, draw a unit square around each visited point. a(n)/A368001(n) is the probability that, when the appropriate number of distinct points have been visited, the drawn squares form a particular one of the fixed polyominoes corresponding to the free polyomino with binary code A246521(n+1).

Can be read as an irregular triangle, whose n-th row contains A000105(n) terms, n >= 1.

			As an irregular triangle:
   1;
   1;
   1, 1;
   1, 4, 1, 1, 1;
  97, 1, 1, 1, 8, 1, 1, 8, 8, 1, 1, 1;
  ...

Index entries for sequences related to polyominoes.

Cf. A000105, A246521, A335573, A367675, A367764, A367994, A367995, A368001 (denominators), A368002, A368004.

a(n)/A368001(n) = (A367994(n)/A367995(n))/A335573(n+1).

A368001 a(n) is the denominator of the probability that a particular one of the A335573(n+1) fixed polyominoes corresponding to the free polyomino with binary code A246521(n+1) appears as the image of a simple random walk on the square lattice.

Original entry on oeis.org

1, 2, 6, 6, 21, 21, 28, 21, 21, 2002, 77, 77, 77, 1001, 77, 77, 1001, 1001, 77, 91, 77, 89089, 785603, 286, 286, 48594, 286, 25924899, 194194, 785603, 194194, 25924899, 286, 89089, 286, 388388, 194194, 286, 51849798, 388388, 194194, 286, 286, 194194, 286, 388388, 286, 286, 194194, 388388, 194194, 286, 388388, 1165164, 291291, 286

Offset: 1

Pontus von Brömssen, Dec 09 2023

In a simple random walk on the square lattice, draw a unit square around each visited point. A368000(n)/a(n) is the probability that, when the appropriate number of distinct points have been visited, the drawn squares form a particular one of the fixed polyominoes corresponding to the free polyomino with binary code A246521(n+1).

Can be read as an irregular triangle, whose n-th row contains A000105(n) terms, n >= 1.

			As an irregular triangle:
     1;
     2;
     6,  6;
    21, 21, 28, 21,   21;
  2002, 77, 77, 77, 1001, 77, 77, 1001, 1001, 77, 91, 77;
  ...

Index entries for sequences related to polyominoes.

Cf. A000105, A246521, A335573, A367676, A367765, A367994, A367995, A368000 (numerators), A368003, A368005.

A368000(n)/a(n) = (A367994(n)/A367995(n))/A335573(n+1).

A367126 a(n) is the degree of the polyomino with binary code A246521(n+1) in the n-omino graph defined in A098891.

Original entry on oeis.org

0, 0, 1, 1, 4, 3, 4, 3, 2, 10, 9, 5, 9, 10, 9, 8, 9, 10, 9, 4, 2, 16, 28, 16, 14, 12, 12, 18, 15, 20, 21, 16, 16, 16, 15, 18, 20, 11, 14, 13, 18, 6, 12, 16, 18, 11, 9, 11, 15, 22, 20, 11, 19, 14, 16, 3, 38, 36, 35, 33, 31, 32, 38, 25, 31, 38, 17, 14, 30, 14, 26

Offset: 1

Pontus von Brömssen, Nov 05 2023

Number of free polyominoes that can be made from the polyomino with binary code A246521(n+1) by moving one of its cells (not counting itself).

Can be read as an irregular triangle, whose m-th row contains A000105(m) terms, m >= 1.

			As an irregular triangle:
   0;
   0;
   1, 1;
   4, 3, 4, 3,  2;
  10, 9, 5, 9, 10, 9, 8, 9, 10, 9, 4, 2;
  ...
For n = 8, A246521(8+1) = 30 is the binary code of the S-tetromino. By moving one cell of the S-tetromino, we can obtain the L, O, and T tetrominoes (but not the I tetromino), so a(8) = 3.

Pontus von Brömssen, Table of n, a(n) for n = 1..6473 (rows 1..10).
Index entries for sequences related to polyominoes.

Cf. A000105, A098891, A246521, A367123, A367124 (row maxima), A367125, A367439, A367443.

a(n) >= A367439(n).

A367443 a(n) is the number of free polyominoes that can be obtained from the polyomino with binary code A246521(n+1) by adding one cell.

Original entry on oeis.org

1, 2, 4, 3, 9, 1, 5, 4, 3, 8, 6, 5, 11, 10, 10, 6, 6, 9, 5, 2, 4, 5, 11, 13, 11, 3, 12, 9, 11, 10, 11, 5, 11, 5, 11, 12, 11, 12, 5, 6, 10, 5, 13, 12, 12, 7, 6, 6, 7, 11, 11, 6, 11, 6, 5, 4, 12, 11, 11, 13, 12, 11, 12, 14, 13, 12, 6, 7, 11, 3, 11, 11, 10, 11

Offset: 1

Pontus von Brömssen, Nov 18 2023

Can be read as an irregular triangle, whose m-th row contains A000105(m) terms, m >= 1.

			As an irregular triangle:
  1;
  2;
  4, 3;
  9, 1, 5,  4,  3;
  8, 6, 5, 11, 10, 10, 6, 6, 9, 5, 2, 4;
  ...
For n = 5, the L tetromino, whose binary code is A246521(5+1) = 15, can be extended to 9 different free pentominoes, so a(5) = 9. (All possible ways to add one cell lead to different pentominoes.)
For n = 6, the square tetromino, whose binary code is A246521(6+1) = 23, can only be extended to the P pentomino by adding one cell, so a(6) = 1.

Pontus von Brömssen, Table of n, a(n) for n = 1..6473 (rows 1..10).
Index entries for sequences related to polyominoes.

Cf. A000105, A246521, A255890 (row minima), A367126, A367439, A367441.

A368392 a(n) is the numerator of the probability that a particular one of the A335573(n+1) fixed polyominoes corresponding to the free polyomino with binary code A246521(n+1) appears in internal diffusion-limited aggregation on the square lattice.

Original entry on oeis.org

1, 1, 1, 1, 1, 4, 17, 1, 1, 57, 5, 5, 5, 73, 5, 5, 73, 73, 5, 1, 5, 49321, 28165117, 5, 5, 169, 5, 123019, 63425, 28165117, 63425, 123019, 5, 49321, 5, 74999, 63425, 5, 58604629, 74999, 63425, 5, 5, 63425, 5, 74999, 5, 5, 63425, 74999, 63425, 5, 74999, 5000341, 32385, 5

Offset: 1

Pontus von Brömssen, Dec 22 2023

See A368386 for details.

Can be read as an irregular triangle, whose n-th row contains A000105(n) terms, n >= 1.

			As an irregular triangle:
   1;
   1;
   1, 1;
   1, 4, 17, 1,  1;
  57, 5,  5, 5, 73, 5, 5, 73, 73, 5, 1, 5;
  ...

Index entries for sequences related to polyominoes.

Cf. A000105, A246521, A335573, A367675, A367764, A368000, A368386, A368387, A368393 (denominators), A368394, A368863 (external diffusion-limited aggregation).

a(n)/A368393(n) = (A368386(n)/A368387(n))/A335573(n+1).

A368393 a(n) is the denominator of the probability that a particular one of the A335573(n+1) fixed polyominoes corresponding to the free polyomino with binary code A246521(n+1) appears in internal diffusion-limited aggregation on the square lattice.

Original entry on oeis.org

1, 2, 6, 6, 35, 35, 140, 35, 35, 1232, 1848, 1848, 1848, 3696, 1848, 1848, 3696, 3696, 1848, 7, 1848, 7386288, 3940584648, 38038, 38038, 5073, 38038, 7217188, 59034976, 3940584648, 59034976, 7217188, 38038, 7386288, 38038, 22138116, 59034976, 38038, 985146162, 22138116, 59034976, 38038, 38038, 59034976, 38038, 22138116, 38038, 38038, 59034976, 22138116, 59034976, 38038, 22138116, 177104928, 3689686, 38038

Offset: 1

Pontus von Brömssen, Dec 22 2023

See A368386 for details.

Can be read as an irregular triangle, whose n-th row contains A000105(n) terms, n >= 1.

			As an irregular triangle:
     1;
     2;
     6,    6;
    35,   35,  140,   35,   35;
  1232, 1848, 1848, 1848, 3696, 1848, 1848, 3696, 3696, 1848, 7, 1848;
  ...

Index entries for sequences related to polyominoes.

Cf. A000105, A246521, A335573, A367676, A367765, A368001, A368386, A368387, A368392 (numerators), A368395, A368863 (external diffusion-limited aggregation).

A368392(n)/a(n) = (A368386(n)/A368387(n))/A335573(n+1).

cp's OEIS Frontend

A367676 a(n) is the denominator of the probability that a particular one of the A335573(n+1) fixed polyominoes corresponding to the free polyomino with binary code A246521(n+1) appears in the version of the Eden growth model described in A367671 when n square cells have been added.

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A367761 a(n) is the denominator of the probability that the free polyomino with binary code A246521(n+1) appears in the Eden growth model on the square lattice, when n square cells have been added.

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A367764 a(n) is the numerator of the probability that a particular one of the A335573(n+1) fixed polyominoes corresponding to the free polyomino with binary code A246521(n+1) appears in the Eden growth model on the square lattice (see A367760), when n square cells have been added.

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A367765 a(n) is the denominator of the probability that a particular one of the A335573(n+1) fixed polyominoes corresponding to the free polyomino with binary code A246521(n+1) appears in the Eden growth model on the square lattice (see A367760), when n square cells have been added.

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A368000 a(n) is the numerator of the probability that a particular one of the A335573(n+1) fixed polyominoes corresponding to the free polyomino with binary code A246521(n+1) appears as the image of a simple random walk on the square lattice.

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A368001 a(n) is the denominator of the probability that a particular one of the A335573(n+1) fixed polyominoes corresponding to the free polyomino with binary code A246521(n+1) appears as the image of a simple random walk on the square lattice.

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A367126 a(n) is the degree of the polyomino with binary code A246521(n+1) in the n-omino graph defined in A098891.

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A367443 a(n) is the number of free polyominoes that can be obtained from the polyomino with binary code A246521(n+1) by adding one cell.

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A368392 a(n) is the numerator of the probability that a particular one of the A335573(n+1) fixed polyominoes corresponding to the free polyomino with binary code A246521(n+1) appears in internal diffusion-limited aggregation on the square lattice.

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