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%I #23 Jun 22 2017 12:11:14
%S 6,28,107,380,1345,4878,18219,69736,271589,1069538,4240351,16877532,
%T 67325913,268902358,1074741203,4297097168,17184391117,68729044938,
%U 274898091975,1099554095044,4398135640001,17592372690878,70369134247867,281475790405560,1125901601341365
%N Numbers of undirected cycles in the 2n-crossed prism graph.
%C Sequence extended via recurrence to start at n = 1. - _Andrew Howroyd_, May 09 2017
%H Andrew Howroyd, <a href="/A234617/b234617.txt">Table of n, a(n) for n = 1..200</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CrossedPrismGraph.html">Crossed Prism Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (10, -37, 64, -52, 16).
%F From _Andrew Howroyd_, May 09 2017 (Start)
%F a(n) = 10*a(n-1)-37*a(n-2)+64*a(n-3)-52*a(n-4)+16*a(n-5) for n>5.
%F G.f.: x*(24*x^4-38*x^3+49*x^2-32*x+6)/((1-4*x)*(x-1)^2*(2*x-1)^2).
%F (End)
%F a(n) = 2^(n-1)+4^n+(2^(n+1)-3)*n. - _Eric W. Weisstein_, May 11 2017
%t Rest@ CoefficientList[Series[x (24 x^4 - 38 x^3 + 49 x^2 - 32 x + 6)/((1 - 4 x) (x - 1)^2*(2 x - 1)^2), {x, 0, 25}], x] (* or *)
%t LinearRecurrence[{10, -37, 64, -52, 16}, {6, 28, 107, 380, 1345}, 25] (* _Michael De Vlieger_, May 09 2017 *)
%t Table[2^(n - 1) + 4^n + (2^(n + 1) - 3) n, {n, 20}] (* _Eric W. Weisstein_, May 11 2017 *)
%o (PARI)
%o Vec((24*x^4-38*x^3+49*x^2-32*x+6)/((1-4*x)*(x-1)^2*(2*x-1)^2)+O(x^50)) \\ _Andrew Howroyd_, May 09 2017
%Y Cf. A137885.
%K nonn
%O 1,1
%A _Eric W. Weisstein_, Dec 28 2013
%E Offset corrected and a(1), a(10)-a(25) from _Andrew Howroyd_, May 09 2017
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