A003750 - OEIS

%I #25 Jun 23 2020 14:32:15

%S 60,8760,617400,36021240,1871009400,90539967480,4181860331640,

%T 187073020183800,8181829090755960,352081040138505720,

%U 14972983484769861240,631272829225942738680,26446059244840564688760,1102721870861189212971000,45821243162927769017364600

%N Number of Hamiltonian paths in K_5 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 Vincenzo Librandi, <a href="/A003750/b003750.txt">Table of n, a(n) for n = 1..600</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_07">Index entries for linear recurrences with constant coefficients</a>, signature (95,-2854,23880,97152,29616,-19296,-6912).

%F a(1) = 60,

%F a(2) = 8760,

%F a(3) = 617400,

%F a(4) = 36021240,

%F a(5) = 1871009400,

%F a(6) = 90539967480,

%F a(7) = 4181860331640,

%F a(8) = 187073020183800, and

%F a(n) = 95a(n-1) - 2854a(n-2) + 23880a(n-3) + 97152a(n-4) + 29616a(n-5) - 19296a(n-6) - 6912a(n-7).

%F G.f.: 60*x*(6912*x^7 -48096*x^6 +39216*x^5 -66112*x^4 +15608*x^3 -726*x^2 +51*x +1)/((12*x^2 +28*x-1)^2*(48*x^3 -90*x^2 -39*x +1)). - _Colin Barker_, Aug 30 2012

%t CoefficientList[Series[60 (6912 x^7 - 48096 x^6 + 39216 x^5 - 66112 x^4 + 15608 x^3 - 726 x^2 + 51 x + 1)/((12 x^2 + 28 x - 1)^2 (48 x^3 - 90 x^2 - 39 x + 1)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 14 2013 *)

%o (PARI) Vec(60*x*(6912*x^7-48096*x^6+39216*x^5-66112*x^4+15608*x^3-726*x^2+51*x+1)/((12*x^2+28*x-1)^2*(48*x^3-90*x^2-39*x+1))+O(x^99)) \\ _Charles R Greathouse IV_, Jun 23 2020

%K nonn,easy

%O 1,1

%A _Frans J. Faase_

%E Added recurrence from Faase's web page. - _N. J. A. Sloane_, Feb 03 2009