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

Author

N. J. A. Sloane, Jan 13 2020

Keywords

• nonn
• tabf
• more

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.

Examples

			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
...
		

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

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

Crossrefs

Cf. A055907-A055915.

Extensions

Name edited by Andrey Zabolotskiy, Jun 21 2022