A091467 Table (by antidiagonals) of unlabeled alternating octupi 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

1,5

References

F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 113 (2.4.41).

Links

Table of n, a(n) for n=1..92.

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))).

Example

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 ...

Crossrefs

Main diagonal: A091468. Row sums: A091468. Cf. A091466.

Sequence in context: A375221 A325492 A266270 * A224861 A050443 A306770

Adjacent sequences: A091464 A091465 A091466 * A091468 A091469 A091470

Keyword

nonn,tabl

Author

Christian G. Bower, Jan 12 2004

Status

approved