A091467 Table (by antidiagonals) of unlabeled alternating octopuses with n black nodes and k white nodes.
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, 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, 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
Offset: 1
Examples
1 1 0 0 0 ... 1 4 3 1 0 ... 0 3 10 9 3 ... 0 1 9 28 28 ... 0 0 3 28 76 ...
References
- F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 113 (2.4.41).
Formula
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))).