A364483 -id:A364483 - cp's OEIS frontend

A364418 The sum of the weights of the stones-and-bones tilings of the (n,2n-4)-benzel, where each stone is given multiplicative weight 3.

3, 102, 10260, 3267540, 3272495580, 10170919805580, 97112573496153540, 2829427113881208115260, 250440846963119234063024220, 67143197168392738521628168122420, 54411613647618445838464808052508179060

Offset: 3

James Propp, Jul 23 2023

nonn

See Problem 17 of the Propp article. It is conjectured that a(n) is 2-adically continuous as a function of n > 4.

J. Propp, Trimer covers in the triangular grid: twenty mostly open problems, to appear.

James Propp, Table of n, a(n) for n = 3..17
James Propp, Trimer covers in the triangular grid: twenty mostly open problems, arXiv:2206.06472 [math.CO], 2022.

Cf. A352207, A364416, A364417, A364438, A364481, A364482, A364483.

A364438 The sum of the weights of the stones-and-bones tilings of the (n,2n-3)-benzel, where each stone is given multiplicative weight 3.

Original entry on oeis.org

9, 270, 27110, 8798490, 8980383330, 28344705113430, 273927748387623390, 8057418594145673168610, 718650987298253553656580570, 193874673319110717570773876192670, 157927323459469084048485672225266775510, 387962431958247267773527802272080627127318890

Offset: 3

James Propp, Jul 24 2023

nonn

See Problem 18 of the Propp article. It is conjectured that a(n) is 2-adically continuous as a function of n > 3.

James Propp, Table of n, a(n) for n = 3..17
James Propp, Trimer covers in the triangular grid: twenty mostly open problems, arXiv:2206.06472 [math.CO], 2022.

Cf. A352207, A364416, A364417, A364418, A364481, A364482, A364483.

A364416 The number of stones-and-bones tilings of the (n,2n-4)-benzel.

Original entry on oeis.org

1, 10, 84, 724, 6516, 60900, 586404, 5777916, 57952212, 589381020, 6060195316, 62863155972, 656765033268, 6902094928308, 72892778268996, 773013952508268, 8226672021670804, 87817595880192684

Offset: 3

James Propp, Jul 23 2023

See Problem 15 of the Propp article. It is conjectured that a(n) is 2-adically continuous as a function of n>4.

James Propp, Trimer covers in the triangular grid: twenty mostly open problems, arXiv:2206.06472 [math.CO], 2022.

Cf. A352207, A364417, A364418, A364438, A364481, A364482, A364483.

More terms from James Propp, Apr 26 2024

A364417 The number of stones-and-bones tilings of the (n,2n-3)-benzel.

Original entry on oeis.org

3, 18, 142, 1266, 12030, 118650, 1198230, 12296202, 127633590, 1336133730, 14079114270, 149124688482, 1586159072814, 16929780310218, 181227223899942, 1944808008842490, 20915277691567206

Offset: 3

James Propp, Jul 23 2023

See Problem 16 of the Propp article. It is conjectured that a(n) is 2-adically continuous as a function of n > 3.

James Propp, Trimer covers in the triangular grid: twenty mostly open problems, arXiv:2206.06472 [math.CO], 2022.

Cf. A352207, A364416, A364418, A364438, A364481, A364482, A364483.

a(15)-a(19) from James Propp, Apr 25 2024

A364481 The number of stones-and-bones tilings of the (3n+1,3n+1)-benzel when one orientation of bone is forbidden.

Original entry on oeis.org

4, 224, 168960, 1705639936, 229940737867776, 413561647491497066496, 9918120959299139713735065600

Offset: 1

James Propp, Jul 26 2023

See Problem 9 of the Propp article. It is conjectured that a(n) is 2-adically continuous as a function of n.

James Propp, Trimer covers in the triangular grid: twenty mostly open problems, arXiv:2206.06472 [math.CO], 2022.

Cf. A352207, A364482, A364483, A364416, A364417, A364418, A364438.

A364482 The number of stones-and-bones tilings of the (3n+1,3n+2)-benzel when one orientation of bone is forbidden.

Original entry on oeis.org

6, 512, 591360, 9160359936, 1897011087409152, 5244422625774526267392, 193403358706333224417833779200, 95098462720808932931887549372170240000

Offset: 1

James Propp, Jul 26 2023

nonn

See Problem 10 of the Propp article. It is conjectured that a(n) is 2-adically continuous as a function of n.

James Propp, Trimer covers in the triangular grid: twenty mostly open problems, arXiv:2206.06472 [math.CO], 2022.

Cf. A352207, A364481, A364483, A364416, A364417, A364418, A364438.

cp's OEIS Frontend

A364418 The sum of the weights of the stones-and-bones tilings of the (n,2n-4)-benzel, where each stone is given multiplicative weight 3.

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A364438 The sum of the weights of the stones-and-bones tilings of the (n,2n-3)-benzel, where each stone is given multiplicative weight 3.

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A364416 The number of stones-and-bones tilings of the (n,2n-4)-benzel.

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A364417 The number of stones-and-bones tilings of the (n,2n-3)-benzel.

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A364481 The number of stones-and-bones tilings of the (3n+1,3n+1)-benzel when one orientation of bone is forbidden.

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A364482 The number of stones-and-bones tilings of the (3n+1,3n+2)-benzel when one orientation of bone is forbidden.

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