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A003740 Number of spanning trees with degrees 1 and 3 in W_5 X P_2n.

%I A003740 #18 Jan 01 2019 06:31:05
%S A003740 208,335344,503672968,757005488704,1137734095903816,
%T A003740 1709944335224262352,2569941155563565968488,3862463470575397280285088,
%U A003740 5805045002479537990606632936
%N A003740 Number of spanning trees with degrees 1 and 3 in W_5 X P_2n.
%D A003740 F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.
%H A003740 Sean A. Irvine, <a href="/A003740/b003740.txt">Table of n, a(n) for n = 1..100</a>
%H A003740 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 A003740 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamiltonian cycles in product graphs</a>
%H A003740 F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>
%H A003740 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F A003740 If b(n) denotes the number of spanning trees with degrees 1 and 3 in W_5 X P_n we have:
%F A003740 b(1) = 0,
%F A003740 b(2) = 208,
%F A003740 b(3) = 0,
%F A003740 b(4) = 335344,
%F A003740 b(5) = 0,
%F A003740 b(6) = 503672968,
%F A003740 b(7) = 0,
%F A003740 b(8) = 757005488704,
%F A003740 b(9) = 0,
%F A003740 b(10) = 1137734095903816,
%F A003740 b(11) = 0,
%F A003740 b(12) = 1709944335224262352,
%F A003740 b(13) = 0,
%F A003740 b(14) = 2569941155563565968488,
%F A003740 b(15) = 0,
%F A003740 b(16) = 3862463470575397280285088,
%F A003740 b(17) = 0,
%F A003740 b(18) = 5805045002479537990606632936,
%F A003740 b(19) = 0,
%F A003740 b(20) = 8724625549856078166453269723376,
%F A003740 b(21) = 0,
%F A003740 b(22) = 13112575518826856642901203139743240,
%F A003740 b(23) = 0,
%F A003740 b(24) = 19707394403851935411114869745719526144,
%F A003740 b(25) = 0,
%F A003740 b(26) = 29619001517386258600018494299567252781896,
%F A003740 b(27) = 0,
%F A003740 b(28) = 44515537310983054901068606912734277302893072,
%F A003740 b(29) = 0,
%F A003740 b(30) = 66904114270101652083096747543361961556161338280,
%F A003740 b(31) = 0,
%F A003740 b(32) = 100552768239022085083137539569611934600600485769824,
%F A003740 b(33) = 0,
%F A003740 b(34) = 151124625306471850563573728012268031905685321872309416,
%F A003740 b(35) = 0,
%F A003740 b(36) = 227131015624872535892492790329036203871753015873169846576,
%F A003740 b(37) = 0,
%F A003740 b(38) = 341363944851262010688127945467040823127463725134532755058760,
%F A003740 b(39) = 0,
%F A003740 b(40) = 513049010606610528824074852666729120665123598849369486838352320,
%F A003740 b(41) = 0,
%F A003740 b(42) = 771081103480659083177648561305159418338110532879217116850112505608,
%F A003740 b(43) = 0,
%F A003740 b(44) = 1158887466602766746036049127283646002598030062997458201209529788050000, and
%F A003740 b(n) = 1498b(n-2) + 9727b(n-4) - 3430420b(n-6) - 51780334b(n-8) + 2175631056b(n-10)
%F A003740 - 3049771912b(n-12) + 20785260864b(n-14) - 885420351008b(n-16) + 2723994857536b(n-18) + 5274700679360b(n-20)
%F A003740 + 125883661338368b(n-22) + 354089303896576b(n-24) - 880465464686592b(n-26) - 28529345908736b(n-28) + 3938132497694720b(n-30)
%F A003740 - 1757770863747072b(n-32) - 1334108047147008b(n-34) - 337906312937472b(n-36) - 49853396680704b(n-38) - 3371549327360b(n-40).
%K A003740 nonn
%O A003740 1,1
%A A003740 _Frans J. Faase_
%E A003740 Added recurrence from Faase's web page. - _N. J. A. Sloane_, Feb 03 2009