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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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%I #17 Jun 21 2022 10:29:05

%S 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,

%T 56,88,98,137,118,145,113,104,79,50,40,17,10,6,0,1

%N 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.

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

%C 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.

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

%H A. J., Guttmann and A. R. Conway, <a href="https://www.semanticscholar.org/paper/Hexagonal-lattice-directed-site-animals-Conway-Guttmann/6904fa94c8ea31414e6f918ace0f38d6038601e3">Hexagonal lattice directed site animals</a>, preprint, 1999.

%e Triangle begins:

%e 1,

%e 1,

%e 1,1,1,

%e 1,2,4,2,0,1,

%e 1,3,4,10,12,14,16,13,14,7,6,4,0,1,

%e 1,4,8,22,37,56,88,98,137,118,145,113,104,79,50,40,17,10,6,0,1

%e ...

%Y Cf. A055907-A055915.

%K nonn,tabf,more

%O 0,7

%A _N. J. A. Sloane_, Jan 13 2020

%E Name edited by _Andrey Zabolotskiy_, Jun 21 2022