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%I #17 Jul 11 2021 10:30:41
%S 70,24400,6912340,1997380720,576043535680,166162145824000,
%T 47929270990315840,13825165615038910720,3987858909906969326080,
%U 1150295005804962553753600,331801758293292909512074240,95707976014178819083415941120,27606896116821809366222931066880
%N Number of 2-factors in K_6 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 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 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (264,7160,-31008,-10480).
%F Recurrence:
%F a(1) = 70,
%F a(2) = 24400,
%F a(3) = 6912340,
%F a(4) = 1997380720, and
%F a(n) = 264a(n-1) + 7160a(n-2) - 31008a(n-3) - 10480a(n-4).
%F G.f.: -10*x*(1048*x^3+3046*x^2-592*x-7)/(10480*x^4+31008*x^3-7160*x^2-264*x+1). [_Colin Barker_, Aug 30 2012]
%p a:= n-> (<<264|7160|-31008|-10480>, <1|0|0|0>, <0|1|0|0>, <0|0|1|0>>^n. <<6912340, 24400, 70, 1>>)[4, 1]: seq(a(n), n=1..15); # _Alois P. Heinz_, Sep 20 2011
%t a[1] = 70; a[2] = 24400; a[3] = 6912340; a[4] = 1997380720; a[n_] := a[n] = 264*a[n-1] + 7160*a[n-2] - 31008*a[n-3] - 10480*a[n-4]; Array[a, 13] (* _Jean-François Alcover_, Mar 18 2014 *)
%t LinearRecurrence[{264,7160,-31008,-10480},{70,24400,6912340,1997380720},20] (* _Harvey P. Dale_, Jul 11 2021 *)
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_, Feb 03 2009
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