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.

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

0,7

Comments

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.

References

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

Links

Table of n, a(n) for n=0..45.

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

Example

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
...

Crossrefs

Cf. A055907-A055915.

Sequence in context: A318222 A209466 A277659 * A258711 A127278 A356165

Adjacent sequences: A331141 A331142 A331143 * A331145 A331146 A331147

Keyword

nonn,tabf,more

Author

N. J. A. Sloane, Jan 13 2020

Extensions

Name edited by Andrey Zabolotskiy, Jun 21 2022

Status

approved