A003693 - OEIS

%I #27 Apr 18 2023 15:26:13

%S 0,2,3,18,54,222,779,2953,10771,40043,147462,545603,2013994,7442927,

%T 27490263,101563680,375176968,1386004383,5120092320,18914660608,

%U 69873991466,258127586367,953569519203,3522660270539

%N Number of 2-factors in P_4 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 Andrew Howroyd, <a href="/A003693/b003693.txt">Table of n, a(n) for n = 1..200</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_05">Index entries for linear recurrences with constant coefficients</a>, signature (2, 7, -2, -3, 1).

%F a(n) = 2a(n-1) + 7a(n-2) - 2a(n-3) - 3a(n-4) + a(n-5), n > 5.

%F G.f.: (-x*(x-1)*(x-2)*(x+1))/(-1 + x^5 - 3*x^4 - 2*x^3 + 7*x^2 + 2*x). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 10 2009

%t LinearRecurrence[{2, 7, -2, -3, 1}, {0, 2, 3, 18, 54}, 30] (* _Jean-François Alcover_, Sep 21 2019 *)

%Y Cf. A003776, A145400, A145415, A145417, A222202, A222203.

%K nonn,easy

%O 1,2

%A _Frans J. Faase_