login
Number of 2-factors in P_6 X P_n.
2

%I #9 Jan 01 2019 06:31:05

%S 0,5,9,222,1140,13903,99051,972080,7826275,71053230,599141127,

%T 5285091303,45349095730,395755191515,3418116104881,29709767180643,

%U 257232791130155,2232466696767889,19346930092499853,167813061128260612,1454798219804865516,12616086588695738786

%N Number of 2-factors in P_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 Andrew Howroyd, <a href="/A145400/b145400.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>

%F a(n) = 5*a(n-1) + 49*a(n-2) - 116*a(n-3) - 363*a(n-4) + 627*a(n-5) + 544*a(n-6) - 1061*a(n-7) + 133*a(n-8) + 264*a(n-9) - 47*a(n-10) - 26*a(n-11) + 3*a(n-12) + a(n-13) for n > 13.

%F G.f.: x^2*(5 - 16*x - 68*x^2 + 169*x^3 + 184*x^4 - 440*x^5 + 41*x^6 + 159*x^7 - 24*x^8 - 21*x^9 + 2*x^10 + x^11)/(1 - 5*x - 49*x^2 + 116*x^3 + 363*x^4 - 627*x^5 - 544*x^6 + 1061*x^7 - 133*x^8 - 264*x^9 + 47*x^10 + 26*x^11 - 3*x^12 - x^13). - _Andrew Howroyd_, Oct 04 2017

%Y Cf. A003693, A222202.

%K nonn

%O 1,2

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

%E Terms a(14) and beyond from _Andrew Howroyd_, Oct 04 2017