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%I #18 May 24 2024 13:11:03
%S 1,12,74,331,1212,3829,10778,27651,65745,146663,309831,624423,1207701,
%T 2252494,4067393,7134576,12191298,20342987,33217622,53174235,83580380,
%U 129177701,196557754,294776792,436141322,637204826,920020667
%N Column 6 of triangle A055907.
%H A. J. Guttmann and A. R. Conway, <a href="https://researchers.ms.unimelb.edu.au/~guttmann@unimelb/articles/hexfinal.pdf">Hexagonal lattice directed site animals</a>, Statistical Physics on the Eve of the Twenty-First Century, ed. M. T. Batchelor, World Scientific, 1999 (H_6 for hexagonal lattices Table 1).
%F G.f.: x^6(1 + 5x + 13x^2 + 40x^3 + 85x^4 + 160x^5 + 297x^6 + 453x^7 + 711x^8 + 956x^9 + 1276x^10 + 1614x^11 + 1798x^12 + 2192x^13 + 2064x^14 + 2446x^15 + 1949x^16 + 2220x^17 + 1546x^18 + 1642x^19 + 1011x^20 + 959x^21 + 558x^22 + 427x^23 + 249x^24 + 135x^25 + 85x^26 + 32x^27 + 15x^28 + 8x^29 + x^31)/((1 - x)^13(1 + x)^6(1 + x^2)^5(1 + x^2 + x^4)^3(1 + x^4)). [See column t6,m in table 1 p. 12 of Guttmann and Conway.]
%Y Cf. A055907.
%K nonn
%O 6,2
%A _Christian G. Bower_, Jun 22 2000