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%I #25 Sep 08 2022 08:44:32
%S 4,156,3832,101476,2653176,69537644,1821675752,47726949876,
%T 1250396334280,32759217743932,858260185404312,22485600623006756,
%U 589101327485494424,15433894026086119116,404353331486123621320,10593672372980858817748,277544131820420163065832,7271392053421269671583068
%N Number of 2-factors in W_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="/A003736/b003736.txt">Table of n, a(n) for n = 1..700</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 (21,149,-285,-1354,1098,-24).
%F a(1) = 4,
%F a(2) = 156,
%F a(3) = 3832,
%F a(4) = 101476,
%F a(5) = 2653176,
%F a(6) = 69537644, and
%F a(n) = 21a(n-1) + 149a(n-2) - 285a(n-3) - 1354a(n-4) + 1098a(n-5) - 24a(n-6).
%F G.f.: -4*x*(x -1)*(6*x^4 -266*x^3 +9*x^2 +19*x +1)/(24*x^6 -1098*x^5 +1354*x^4 +285*x^3 -149*x^2 -21*x +1). - _Colin Barker_, Aug 30 2012
%t CoefficientList[Series[-4 (x - 1) (6 x^4 - 266 x^3 + 9 x^2 + 19 x + 1)/(24 x^6 - 1098 x^5 + 1354 x^4 + 285 x^3 - 149 x^2 - 21 x + 1), {x, 0, 40}], x] (* _Vincenzo Librandi_, Oct 14 2013 *)
%o (Magma) I:=[4,156,3832,101476,2653176,69537644]; [n le 6 select I[n] else 21*Self(n-1)+149*Self(n-2)-285*Self(n-3)-1354*Self(n-4)+1098*Self(n-5)-24*Self(n-6): n in [1..20]]; // _Vincenzo Librandi_, Oct 14 2013
%o (PARI) Vec(-4*x*(x-1)*(6*x^4-266*x^3+9*x^2+19*x+1)/(24*x^6-1098*x^5+1354*x^4+285*x^3-149*x^2-21*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
%E More terms from _Vincenzo Librandi_, Oct 14 2013
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