cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

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

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Author

Pontus von Brömssen, Dec 09 2023

Keywords

Comments

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.

Examples

			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;
  ...
		

Crossrefs

Formula

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

A368005 Denominator of the greatest probability that a particular fixed polyomino with n cells appears as the image of a simple random walk on the square lattice.

Original entry on oeis.org

1, 2, 6, 21, 2002, 48594, 6786340869, 60683548875931642773982870, 148748699073930002409397035, 98235230940726955523493708384725766221632599616516980478369143134298250712431827891413914221729825
Offset: 1

Views

Author

Pontus von Brömssen, Dec 21 2023

Keywords

Comments

a(n) is the denominator of the maximum of A368000/A368001 over the n-th row. See A368000 for details.

Examples

			See A368004.
		

Crossrefs

A367997 Denominator of the least probability that a particular free polyomino with n cells appears as the image of a simple random walk on the square lattice.

Original entry on oeis.org

1, 1, 3, 21, 91, 291291, 17574557, 1433685253, 2819787, 14870951705, 124958680680282, 3525784478869018946300814, 27359333221
Offset: 1

Views

Author

Pontus von Brömssen, Dec 08 2023

Keywords

Comments

a(n) is the denominator of the minimum of A367994/A367995 over the n-th row. See A367994 for details.

Crossrefs

Cf. A367994, A367995, A367996 (numerators), A367999, A368003.

A368002 Numerator of the least probability that a particular fixed polyomino with n cells appears as the image of a simple random walk on the square lattice.

Original entry on oeis.org

1, 1, 1, 1, 8, 412, 54, 59309, 176087633490076859, 18569, 81059275440235943, 1615066814060816060766626689229243976663152060069, 5644184595206308867273871
Offset: 1

Views

Author

Pontus von Brömssen, Dec 09 2023

Keywords

Comments

a(n) is the numerator of the minimum of A368000/A368001 over the n-th row. See A368000 for details.

Crossrefs

Cf. A367996, A368000, A368001, A368003 (denominators), A368004.
Showing 1-4 of 4 results.