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A003732 Number of Hamiltonian paths in C_5 X P_n.

%I A003732 #17 Jan 01 2019 06:31:05
%S A003732 5,130,1660,16820,152230,1275680,10154290,77897010,581452680,
%T A003732 4250594690,30572999140,217099260110,1525905283670,10636695448300,
%U A003732 73649615037480,507171127397480,3476871213780220,23747634842538120
%N A003732 Number of Hamiltonian paths in C_5 X P_n.
%D A003732 F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.
%H A003732 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 A003732 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamiltonian cycles in product graphs</a>
%H A003732 F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>
%F A003732 Faase gives a 12-term linear recurrence on his web page:
%F A003732 a(1) = 5,
%F A003732 a(2) = 130,
%F A003732 a(3) = 1660,
%F A003732 a(4) = 16820,
%F A003732 a(5) = 152230,
%F A003732 a(6) = 1275680,
%F A003732 a(7) = 10154290,
%F A003732 a(8) = 77897010,
%F A003732 a(9) = 581452680,
%F A003732 a(10) = 4250594690,
%F A003732 a(11) = 30572999140,
%F A003732 a(12) = 217099260110,
%F A003732 a(13) = 1525905283670,
%F A003732 a(14) = 10636695448300 and
%F A003732 a(n) = 19a(n-1) - 127a(n-2) + 328a(n-3) - 117a(n-4) - 675a(n-5)
%F A003732 + 1127a(n-6) - 1016a(n-7) + 380a(n-8) + 12a(n-9) - 140a(n-10)
%F A003732 + 68a(n-11) - 20a(n-12), n>14.
%F A003732 G.f. 5*x+130*x^2 -10*x^3*(-166 +1472*x -4347*x^2 +2503*x^3 +7316*x^4 -13386*x^5 +12513*x^6 -4715*x^7 -215*x^8 +1824*x^9 -856*x^10 +252*x^11)  / ( (1-7*x-x^2+20*x^3-3*x^4+3*x^5+5*x^6) *(-1+6*x-4*x^2+2*x^3)^2 ). - _R. J. Mathar_, Aug 21 2012
%K A003732 nonn
%O A003732 1,1
%A A003732 _Frans J. Faase_
%E A003732 Added recurrence from Faase's web page. - _N. J. A. Sloane_, Feb 03 2009