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%I #8 Jan 07 2023 09:28:13
%S 1,6,22,63,151,316,596,1037,1693,2626,3906,5611,7827,10648,14176,
%T 18521,23801,30142,37678,46551,56911,68916,82732,98533,116501,136826,
%U 159706,185347,213963,245776,281016,319921,362737,409718,461126,517231,578311,644652,716548,794301
%N Number of cycles in the n-dipyramidal graph.
%C Extended to a(1)-a(2) using the formula/recurrence.
%C For n > 2, also the number of minimal edge cuts in the n-prism graph. - _Eric W. Weisstein_, Jan 07 2023
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DipyramidalGraph.html">Dipyramidal Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MinimalEdgeCut.html">Minimal Edge Cut</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrismGraph.html">Prism Graph</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5, -10, 10, -5, 1).
%F a(n) = n*(n - 1)*(2*n^2 - 4*n + 15)/6 + 1.
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
%F G.f.: x (-1 - x - 2*x^2 - 3*x^3 - x^4)/(-1 + x)^5.
%t LinearRecurrence[{5, -10, 10, -5, 1}, {1, 6, 22, 63, 151}, 20]
%t Table[n (n - 1) (2 n^2 - 4 n + 15)/6 + 1, {n, 20}]
%t CoefficientList[Series[(-1 - x - 2 x^2 - 3 x^3 - x^4)/(-1 + x)^5, {x, 0, 20}], x]
%K nonn,easy
%O 1,2
%A _Eric W. Weisstein_, Apr 19 2019