A055915 -id:A055915 - cp's OEIS frontend

A055918 Coefficients of a polynomial used in calculation of A055915.

1, 8, 36, 156, 524, 1552, 4259, 10394, 24183, 51875, 106494, 206745, 384905, 687199, 1183788, 1963561, 3173730, 4927653, 7548433, 11034284, 16135051, 22312164, 31309061, 41115663, 55583921, 69539866, 90846746, 108550608, 137370735

Offset: 0

Christian G. Bower, Jun 22 2000

Last term has index 80.

Georg Fischer, Table of n, a(n) for n = 0..80
A. J. Guttmann and A. R. Conway, Hexagonal lattice directed site animals, Statistical Physics on the Eve of the Twenty-First Century, ed. M. T. Batchelor, World Scientific, 1999 (t_9,m for hexagonal lattices, Table 1).

Corrected by R. J. Mathar, Oct 31 2006

A055907 Triangle: number of directed site animals on hexagonal net (honeycomb) with n total sites and k sites supported in one particular way.

Original entry on oeis.org

0, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 6, 10, 6, 1, 1, 9, 21, 20, 8, 1, 1, 12, 39, 53, 36, 10, 1, 1, 16, 67, 121, 128, 56, 12, 1, 1, 20, 107, 249, 388, 240, 74, 14, 1, 1, 25, 163, 471, 1050, 854, 331, 100, 16, 1, 1, 30, 238, 836, 2601, 2654, 1212, 511, 130, 18, 1, 1, 36, 337

Offset: 0

Christian G. Bower, Jun 14 2000

			Table begins:
  0;
  1,  1;
  1,  2,  1;
  1,  4,  4,  1;
  1,  6, 10,  6,  1;
  ...

A. J. Guttmann, Indicators of solvability for lattice models, Discrete Math., 217 (2000), 167-189 (A_h of Section 6).
A. J. Guttmann and A. R. Conway, Hexagonal lattice directed site animals, Statistical Physics on the Eve of the Twenty-First Century, ed. M. T. Batchelor, World Scientific, 1999 (F_h of Section 4).

Row sums give A055919.
Columns 1-9 give: A002620(n+1), A055908, A055909, A055910, A055911, A055912, A055913, A055914, A055915.
Cf. A055898.

Name edited by Andrey Zabolotskiy, Jun 21 2022

A331144 Irregular triangle read by rows: row n gives coefficients (in increasing order of powers of x) of normalized numerator polynomial of generating function for hexagonal net (honeycomb) directed site animals. Here n is the number of sites supported in one particular way.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 2, 4, 2, 0, 1, 1, 3, 4, 10, 12, 14, 16, 13, 14, 7, 6, 4, 0, 1, 1, 4, 8, 22, 37, 56, 88, 98, 137, 118, 145, 113, 104, 79, 50, 40, 17, 10, 6, 0, 1

Offset: 0

N. J. A. Sloane, Jan 13 2020

Guttmann-Conway give coefficients for rows n <= 9.

This triangle just gives the numerators of the generating functions. Although it is not clear from their descriptions, it appears that A055907-A055915 give the expansions of the actual generating functions.

			Triangle begins:
1,
1,
1,1,1,
1,2,4,2,0,1,
1,3,4,10,12,14,16,13,14,7,6,4,0,1,
1,4,8,22,37,56,88,98,137,118,145,113,104,79,50,40,17,10,6,0,1
...

Guttmann, A. J., and A. R. Conway. "Hexagonal lattice directed site animals." Series on advances in statistical mechanics, 14.1 (1999): 491-504.

A. J., Guttmann and A. R. Conway, Hexagonal lattice directed site animals, preprint, 1999.

Cf. A055907-A055915.

Name edited by Andrey Zabolotskiy, Jun 21 2022

cp's OEIS Frontend

A055918 Coefficients of a polynomial used in calculation of A055915.

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A055907 Triangle: number of directed site animals on hexagonal net (honeycomb) with n total sites and k sites supported in one particular way.

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A331144 Irregular triangle read by rows: row n gives coefficients (in increasing order of powers of x) of normalized numerator polynomial of generating function for hexagonal net (honeycomb) directed site animals. Here n is the number of sites supported in one particular way.

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Author

Keywords

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Examples

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Links

Crossrefs

Extensions