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A003734 Number of spanning trees with degrees 1 and 3 in C_5 X P_2n.

%I A003734 #20 Jan 01 2019 06:31:05
%S A003734 0,260,27420,2504560,223723080,19923617840,1773563554900,
%T A003734 157870122686600,14052371971981100,1250831588811052320,
%U A003734 111339169110472830220,9910535055491682625400,882157695038695625086700,78522722964255506997330800,6989473714324564174042717340
%N A003734 Number of spanning trees with degrees 1 and 3 in C_5 X P_2n.
%D A003734 F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.
%H A003734 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 A003734 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamiltonian cycles in product graphs</a>
%H A003734 F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>
%H A003734 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F A003734 Faase gives a 12-term linear recurrence on his web page:
%F A003734 If b(n) denotes the number of spanning trees with degrees 1 and 3 in C_5 X P_n we have:
%F A003734 b(1) = 0,
%F A003734 b(2) = 0,
%F A003734 b(3) = 0,
%F A003734 b(4) = 260,
%F A003734 b(5) = 0,
%F A003734 b(6) = 27420,
%F A003734 b(7) = 0,
%F A003734 b(8) = 2504560,
%F A003734 b(9) = 0,
%F A003734 b(10) = 223723080,
%F A003734 b(11) = 0,
%F A003734 b(12) = 19923617840,
%F A003734 b(13) = 0,
%F A003734 b(14) = 1773563554900,
%F A003734 b(15) = 0,
%F A003734 b(16) = 157870122686600,
%F A003734 b(17) = 0,
%F A003734 b(18) = 14052371971981100,
%F A003734 b(19) = 0,
%F A003734 b(20) = 1250831588811052320,
%F A003734 b(21) = 0,
%F A003734 b(22) = 111339169110472830220,
%F A003734 b(23) = 0,
%F A003734 b(24) = 9910535055491682625400,
%F A003734 b(25) = 0,
%F A003734 b(26) = 882157695038695625086700, and
%F A003734 b(n) = 98b(n-2) - 745b(n-4) - 4916b(n-6) - 234b(n-8) + 160624b(n-10)
%F A003734 - 26648b(n-12) + 338976b(n-14) - 1265216b(n-16) - 2291392b(n-18) - 1695488b(n-20)
%F A003734 - 307200b(n-22) + 32768b(n-24).
%K A003734 nonn
%O A003734 1,2
%A A003734 _Frans J. Faase_
%E A003734 Added recurrence from Faase's web page. - _N. J. A. Sloane_, Feb 03 2009
%E A003734 More terms from _Sean A. Irvine_, Jul 29 2015