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%I #21 Jun 21 2022 08:57:10
%S 0,1,1,1,2,1,1,4,4,1,1,6,10,6,1,1,9,21,20,8,1,1,12,39,53,36,10,1,1,16,
%T 67,121,128,56,12,1,1,20,107,249,388,240,74,14,1,1,25,163,471,1050,
%U 854,331,100,16,1,1,30,238,836,2601,2654,1212,511,130,18,1,1,36,337
%N Triangle: number of directed site animals on hexagonal net (honeycomb) with n total sites and k sites supported in one particular way.
%H A. J. Guttmann, <a href="https://doi.org/10.1016/S0012-365X(99)00262-9">Indicators of solvability for lattice models</a>, Discrete Math., 217 (2000), 167-189 (A_h of Section 6).
%H A. J. Guttmann and A. R. Conway, <a href="https://blogs.unimelb.edu.au/tony-guttmann/files/2019/09/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 (F_h of Section 4).
%e Table begins:
%e 0;
%e 1, 1;
%e 1, 2, 1;
%e 1, 4, 4, 1;
%e 1, 6, 10, 6, 1;
%e ...
%Y Row sums give A055919.
%Y Columns 1-9 give: A002620(n+1), A055908, A055909, A055910, A055911, A055912, A055913, A055914, A055915.
%Y Cf. A055898.
%K nonn,tabl
%O 0,5
%A _Christian G. Bower_, Jun 14 2000
%E Name edited by _Andrey Zabolotskiy_, Jun 21 2022
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