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%I #7 Jun 09 2019 06:00:20
%S 0,0,1,8,45,242,1414,9432,72246,628260,6116319,65856928,776628203,
%T 9950798214,137612550620,2042588039056,32384583304092,546155914771464,
%U 9761655297881037,184309987662192600,3665514979650544153,76586509823743735706,1677182881414143407490
%N Number of (undirected) cycles in the n-triangular honeycomb rook graph.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%F a(n) = sum(k=1..n,A002807(k)).
%F a(n) ~ exp(1) * (n-1)! / 2. - _Vaclav Kotesovec_, Jun 09 2019
%t Table[Sum[Binomial[k, l] (l - 1)!, {k, n}, {l, 3, k}]/2, {n, 20}]
%t Table[Sum[k (2 HypergeometricPFQ[{1, 1, 1 - k}, {2}, -1] - k - 1)/4, {k, n}], {n, 20}]
%Y Cf. A002807 (cycles in the complete graph).
%K nonn
%O 1,4
%A _Eric W. Weisstein_, Jul 14 2017
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