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 1-6 of 6 results.

A367672 a(n) is the denominator of the probability that 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.

Original entry on oeis.org

1, 1, 3, 3, 14, 21, 84, 21, 12, 1008, 126, 21, 315, 5040, 126, 126, 2016, 1008, 126, 672, 60, 99792, 4989600, 1155, 3780, 9072, 66, 30240, 3360, 4536, 554400, 453600, 60, 45360, 60, 277200, 498960, 66, 5184, 9072, 45360, 189, 13860, 554400, 4620, 50400, 1260, 3465, 73920, 712800, 554400, 3465, 12960, 12600, 453600, 360
Offset: 1

Views

Author

Pontus von Brömssen, Nov 26 2023

Keywords

Comments

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.

Examples

			As an irregular triangle:
     1;
     1;
     3,   3;
    14,  21, 84,  21,   12;
  1008, 126, 21, 315, 5040, 126, 126, 2016, 1008, 126, 672, 60;
  ...

Links

Crossrefs

Cf. A000105, A246521, A335573, A367671 (numerators), A367674, A367675, A367676, A367761.

Formula

A367671(n)/a(n) = (A367675(n)/A367676(n))*A335573(n+1).

A367673 Numerator of the greatest probability that a particular free polyomino with n cells appears in the version of the Eden growth model described in A367671.

Original entry on oeis.org

1, 1, 2, 5, 253, 2657, 1839533, 11611594193, 119221101341, 3152002318138937, 2390156990671551019, 391219943696485871537172611, 1374972518894998705708792681, 21138479762006403022428257137861
Offset: 1

Views

Author

Pontus von Brömssen, Nov 26 2023

Keywords

Comments

a(n) is the numerator of the maximum of A367671/A367672 over the n-th row.

Examples

			For 1 <= n <= 14, the following are the unique polyominoes that have the maximum probabilities for their respective sizes:
                    _      _      _
        _    _     | |    | |_   | |_ _
   _   | |  | |_   | |_   |   |  |    _|
  |_|  |_|  |_ _|  |_ _|  |_ _|  |_ _|
                                      _ _
     _          _          _ _      _|   |_
   _| |_ _    _| |_ _    _|   |_   |      _|
  |_     _|  |      _|  |      _|  |_ _  |
    |_ _|    |_ _ _|    |_ _ _|        |_|
                           _          _
     _ _      _ _ _       | |_      _| |_
   _|   |_   |     |_    _|   |_   |     |_
  |      _|  |      _|  |       |  |       |
  |_    |    |_    |    |_     _|  |_     _|
    |_ _|      |_ _|      |_ _|      |_ _|

Links

Crossrefs

Cf. A367671, A367672, A367674 (denominators), A367677, A367762.

A367678 Denominator of the greatest probability that a particular fixed polyomino with n cells appears in the version of the Eden growth model described in A367671.

Original entry on oeis.org

1, 2, 6, 21, 672, 18144, 32659200, 204120000, 12243879648000, 550274933894400000, 5577105239386480800000, 870028417344291004800000, 51097100257451535417918627840000, 292528465778659685432564243496960000000
Offset: 1

Views

Author

Pontus von Brömssen, Nov 26 2023

Keywords

Comments

a(n) is the denominator of the maximum of A367675/A367676 over the n-th row.

Links

Crossrefs

Cf. A367671, A367674, A367675, A367676, A367677 (numerators), A367767.

A367763 Denominator of the greatest probability that a particular free polyomino with n cells appears in the Eden growth model (see A367760).

Original entry on oeis.org

1, 1, 3, 3, 5, 900, 756000, 15876000, 42674688000, 56899584000, 1204450394112000, 2782280410398720000, 154249625952505036800000, 61082851877191994572800000
Offset: 1

Views

Author

Pontus von Brömssen, Dec 02 2023

Keywords

Comments

a(n) is the denominator of the maximum of A367760/A367761 over the n-th row.

Links

Crossrefs

Cf. A367674, A367760, A367761, A367762 (numerators), A367767.

A367999 Denominator of the greatest 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, 1001, 24297, 154359847292651, 30341774437965821386991435, 92319517852923871319659686774769508009256168960677900730, 50934152340027691948241452572262612821964943639897156747372521002131242728356002575294796863242927131886444334117126282630281250
Offset: 1

Views

Author

Pontus von Brömssen, Dec 08 2023

Keywords

Comments

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

Examples

			See A367998.

Links

Crossrefs

Cf. A367674, A367763, A367994, A367995, A367997, A367998 (numerators), A368005.

A368391 Denominator of the greatest probability that a particular free polyomino with n cells appears in internal diffusion-limited aggregation on the square lattice.

Original entry on oeis.org

1, 1, 3, 35, 154, 492573081, 2263639868336, 2851008421256134796827810712799257125795200, 23733667150026775615685852367392733768076432660227006271200, 153969151852607771689295889934692329991676103836044675654575411018653133479482476448000
Offset: 1

Views

Author

Pontus von Brömssen, Dec 22 2023

Keywords

Comments

a(n) is the denominator of the maximum of A368386/A368387 over the n-th row. See A368386 for details.

Examples

			See A368390.

Links

Crossrefs

Cf. A367674, A367763, A367999, A368386, A368387, A368389, A368390 (numerators), A368395, A368662 (external diffusion-limited aggregation).
Showing 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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