A289896 Number of (undirected) cycles in the n-triangular honeycomb rook graph.

0, 0, 1, 8, 45, 242, 1414, 9432, 72246, 628260, 6116319, 65856928, 776628203, 9950798214, 137612550620, 2042588039056, 32384583304092, 546155914771464, 9761655297881037, 184309987662192600, 3665514979650544153, 76586509823743735706, 1677182881414143407490

Offset

1,4

Links

Table of n, a(n) for n=1..23.

Eric Weisstein's World of Mathematics, Graph Cycle

Formula

a(n) = sum(k=1..n,A002807(k)).

a(n) ~ exp(1) * (n-1)! / 2. - Vaclav Kotesovec, Jun 09 2019

Mathematica

Table[Sum[Binomial[k, l] (l - 1)!, {k, n}, {l, 3, k}]/2, {n, 20}]
Table[Sum[k (2 HypergeometricPFQ[{1, 1, 1 - k}, {2}, -1] - k - 1)/4, {k, n}], {n, 20}]

Crossrefs

Cf. A002807 (cycles in the complete graph).

Sequence in context: A368576 A055422 A204618 * A367435 A006887 A009369

Adjacent sequences: A289893 A289894 A289895 * A289897 A289898 A289899

Keyword

nonn

Author

Eric W. Weisstein, Jul 14 2017

Status

approved