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%I #28 Mar 03 2024 10:36:40
%S 75,128625,199065600,307147367625,473862674071875,731065883885568000,
%T 1127873690900648512275,1740060755637940344737625,
%U 2684530596730102104276172800
%N Number of spanning trees in (K_5 - e) X P_n.
%D F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.
%H P. Raff, <a href="/A003745/b003745.txt">Table of n, a(n) for n = 1..200</a>
%H 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 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamiltonian cycles in product graphs</a>
%H F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>
%H P. Raff, <a href="http://arxiv.org/abs/0809.2551">Spanning Trees in Grid Graphs</a>, arXiv:0809.2551 [math.CO], 2008.
%H P. Raff, <a href="http://www.math.rutgers.edu/~praff/span/5/12-13-14-15-23-24-25-34-35/index.xml">Analysis of the Number of Spanning Trees of G x P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {2, 5}, {3, 4}}.</a> Contains sequence, recurrence, generating function, and more.
%H 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 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1645, -160129, 3747310, -7579606, 3747310, -160129, 1645, -1).
%F a(n) = 1645*a(n-1) - 160129*a(n-2) + 3747310*a(n-3) - 7579606*a(n-4) + 3747310*a(n-5) - 160129*a(n-6) + 1645*a(n-7) - a(n-8). - Modified by _Paul Raff_, Oct 29 2009
%F G.f.: -75x(x^6 + 70x^5 - 6838x^4 + 6838x^2 - 70x - 1)/(x^8 - 1645x^7 + 160129x^6 - 3747310x^5 + 7579606x^4 - 3747310x^3 + 160129x^2 - 1645x + 1). - _Paul Raff_, Oct 29 2009
%F a(n) = 75*A001906(n)*(A004187(n))^3 [_R. K. Guy_, via seqfan list, Mar 28 2009]. - _R. J. Mathar_, Jun 03 2009
%t 75 LinearRecurrence[{1645, -160129, 3747310, -7579606, 3747310, -160129, 1645, -1}, {1, 1715, 2654208, 4095298235, 6318168987625, 9747545118474240, 15038315878675313497, 23200810075172537929835}, 20] (* _Jean-François Alcover_, Oct 07 2018 *)
%K nonn
%O 1,1
%A _Frans J. Faase_
%E Added recurrence from Faase's web page. - _N. J. A. Sloane_, Feb 03 2009
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