login
Number of spanning trees with degrees 1 and 3 in S_4 X P_{2n-1}.
0

%I #23 Jan 27 2019 21:33:10

%S 1,0,24,54,492,1944,11976,57024,313440,1587168,8417472,43483392,

%T 227995008,1185394176,6192642048,32263570944,168350991360,

%U 877689686016,4578049517568,23872537976832,124504626978816,649282059657216,3386128302882816,17658788068196352

%N Number of spanning trees with degrees 1 and 3 in S_4 X P_{2n-1}.

%D F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.

%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/Tra#trees">Index entries for sequences related to trees</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2, 16, 4).

%F a(n) = 2*a(n-1) + 16*a(n-2) + 4*a(n-3), n > 4.

%F G.f.: x*(1 + 8*x^2 + 2*x^3 - 2*x)/(1 - 2*x - 16*x^2 - 4*x^3). - _R. J. Mathar_, Dec 16 2008

%t Join[{1,0},LinearRecurrence[{2,16,4},{24,54,492},20]] (* _Harvey P. Dale_, Mar 17 2013 *)

%K nonn,easy

%O 1,3

%A _Frans J. Faase_; corrections Feb 07 2009