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Number of 2-factors in O_6 X P_n.
1

%I #15 Jan 01 2019 06:31:05

%S 20,2984,340852,40071100,4696965476,550730736140,64572426811780,

%T 7571054816109868,887698562638519076,104081767587749759756,

%U 12203482981057263416260,1430846154730977823707628,167765278289617542860512868,19670310820391775621430114508

%N Number of 2-factors in O_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 Alois P. Heinz, <a href="/A145405/b145405.txt">Table of n, a(n) for n = 1..150</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 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (113,585,-10329,17644,3148,-8496).

%F Recurrence:

%F a(1) = 20,

%F a(2) = 2984,

%F a(3) = 340852,

%F a(4) = 40071100,

%F a(5) = 4696965476,

%F a(6) = 550730736140, and

%F a(n) = 113a(n-1) + 585a(n-2) - 10329a(n-3) + 17644a(n-4) + 3148a(n-5) - 8496a(n-6).

%F G.f.: -4*x*(2124*x^5-403*x^4-3941*x^3+2010*x^2-181*x-5) / (8496*x^6 -3148*x^5 -17644*x^4 +10329*x^3 -585*x^2 -113*x+1). [_Colin Barker_, Aug 23 2012]

%p a:= n-> (Matrix (6, (i, j)-> `if` (i=j-1, 1, `if` (i=6, [-8496, 3148, 17644, -10329, 585, 113][j], 0)))^n. <<1, 20, 2984, 340852, 40071100, 4696965476>>) [1, 1]: seq (a(n), n=1..20); # _Alois P. Heinz_, Aug 28, 2011

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_, Feb 03 2009