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A091467 Table (by antidiagonals) of unlabeled alternating octopuses with n black nodes and k white nodes.

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%I A091467 #6 Sep 05 2025 00:22:29
%S A091467 1,1,1,0,4,0,0,3,3,0,0,1,10,1,0,0,0,9,9,0,0,0,0,3,28,3,0,0,0,0,1,28,
%T A091467 28,1,0,0,0,0,0,15,76,15,0,0,0,0,0,0,3,90,90,3,0,0,0,0,0,0,1,55,238,
%U A091467 55,1,0,0,0,0,0,0,0,18,297,297,18,0,0,0,0,0,0,0,0,3,219,736,219,3,0,0,0,0,0
%N A091467 Table (by antidiagonals) of unlabeled alternating octopuses with n black nodes and k white nodes.
%D A091467 F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 113 (2.4.41).
%F A091467 G.f.: A(x, y) = Sum_{k>=1} (phi(k)/k)*log((1-x^n*y^n)^2/(1-x^n*y^n*(3+x^n+y^n))).
%e A091467 1  1  0  0  0 ...
%e A091467 1  4  3  1  0 ...
%e A091467 0  3 10  9  3 ...
%e A091467 0  1  9 28 28 ...
%e A091467 0  0  3 28 76 ...
%Y A091467 Main diagonal: A091468. Row sums: A091468. Cf. A091466.
%K A091467 nonn,tabl,changed
%O A091467 1,5
%A A091467 _Christian G. Bower_, Jan 12 2004