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

Author

Eric W. Weisstein, Jul 14 2017

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Graph Cycle

Crossrefs

Cf. A002807 (cycles in the complete graph).

Programs

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}]

Formula

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

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