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%I A167058 #12 Aug 23 2023 09:44:16
%S A167058 3,945,221184,50055705,11275732875,2538325278720,571357349020731,
%T A167058 128606300878893705,28947814696524275712,6515821689652895090625,
%U A167058 1466636804229895456081107,330123137841949620861665280,74306935243221668928140352051
%N A167058 Number of spanning trees in (S_5 + e) X P_n.
%D A167058 F. Faase, On the number of specific spanning subgraphs of the graphs A X P_n, Ars Combin. 49 (1998), 129-154.
%H A167058 P. Raff, <a href="/A167058/b167058.txt">Table of n, a(n) for n = 1..200</a>
%H A167058 F. Faase, <a href="http://www.iwriteiam.nl/Cpaper.zip">On the number of specific spanning subgraphs of the graphs G X P_n</a>, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.
%H A167058 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamiltonian cycles in product graphs</a>
%H A167058 F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>
%H A167058 P. Raff, <a href="http://arxiv.org/abs/0809.2551">Spanning Trees in Grid Graphs</a>, arXiv:0809.2551 [math.CO], 2008.
%H A167058 P. Raff, <a href="http://www.math.rutgers.edu/~praff/span/5/12-13-14-15-23/index.xml">Analysis of the Number of Spanning Trees of (S_5 + e) x P_n</a>. Contains sequence, recurrence, generating function, and more.
%H A167058 P. Raff, <a href="http://www.myraff.com/projects/spanning-trees-in-grid-graphs">Analysis of the Number of Spanning Trees of Grid Graphs</a>.
%H A167058 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%H A167058 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (270,-10529,95310,-177156,95310,-10529,270,-1).
%F A167058 a(n) = 270 a(n-1)
%F A167058 - 10529 a(n-2)
%F A167058 + 95310 a(n-3)
%F A167058 - 177156 a(n-4)
%F A167058 + 95310 a(n-5)
%F A167058 - 10529 a(n-6)
%F A167058 + 270 a(n-7)
%F A167058 - a(n-8)
%F A167058 G.f.: -3x(x^6 +45x^5 -793x^4 +793x^2 -45x -1)/ (x^8 -270x^7 +10529x^6 -95310x^5 +177156x^4 -95310x^3 +10529x^2 -270x +1)
%t A167058 CoefficientList[Series[-3x (x^6+45x^5-793x^4+793x^2-45x-1)/(x^8-270x^7+ 10529x^6-95310x^5+177156x^4-95310x^3+10529x^2-270x+1),{x,0,30}],x] (* or *) LinearRecurrence[{270,-10529,95310,-177156,95310,-10529,270,-1},{0,3,945,221184,50055705,11275732875,2538325278720,571357349020731},30] (* _Harvey P. Dale_, Nov 22 2021 *)
%K A167058 nonn
%O A167058 1,1
%A A167058 _Paul Raff_

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