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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 lattice directed site animals. Here n is the number of sites supported in one particular way. 0
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 (list; graph; refs; listen; history; text; internal format)
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 A335764

Adjacent sequences:  A331141 A331142 A331143 * A331145 A331146 A331147

KEYWORD

nonn,tabf,more

AUTHOR

N. J. A. Sloane, Jan 13 2020

STATUS

approved

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Last modified August 14 01:28 EDT 2020. Contains 336473 sequences. (Running on oeis4.)