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

%I #18 Jan 01 2019 06:31:05

%S 208,335344,503672968,757005488704,1137734095903816,

%T 1709944335224262352,2569941155563565968488,3862463470575397280285088,

%U 5805045002479537990606632936

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

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

%H Sean A. Irvine, <a href="/A003740/b003740.txt">Table of n, a(n) for n = 1..100</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/Tra#trees">Index entries for sequences related to trees</a>

%F If b(n) denotes the number of spanning trees with degrees 1 and 3 in W_5 X P_n we have:

%F b(1) = 0,

%F b(2) = 208,

%F b(3) = 0,

%F b(4) = 335344,

%F b(5) = 0,

%F b(6) = 503672968,

%F b(7) = 0,

%F b(8) = 757005488704,

%F b(9) = 0,

%F b(10) = 1137734095903816,

%F b(11) = 0,

%F b(12) = 1709944335224262352,

%F b(13) = 0,

%F b(14) = 2569941155563565968488,

%F b(15) = 0,

%F b(16) = 3862463470575397280285088,

%F b(17) = 0,

%F b(18) = 5805045002479537990606632936,

%F b(19) = 0,

%F b(20) = 8724625549856078166453269723376,

%F b(21) = 0,

%F b(22) = 13112575518826856642901203139743240,

%F b(23) = 0,

%F b(24) = 19707394403851935411114869745719526144,

%F b(25) = 0,

%F b(26) = 29619001517386258600018494299567252781896,

%F b(27) = 0,

%F b(28) = 44515537310983054901068606912734277302893072,

%F b(29) = 0,

%F b(30) = 66904114270101652083096747543361961556161338280,

%F b(31) = 0,

%F b(32) = 100552768239022085083137539569611934600600485769824,

%F b(33) = 0,

%F b(34) = 151124625306471850563573728012268031905685321872309416,

%F b(35) = 0,

%F b(36) = 227131015624872535892492790329036203871753015873169846576,

%F b(37) = 0,

%F b(38) = 341363944851262010688127945467040823127463725134532755058760,

%F b(39) = 0,

%F b(40) = 513049010606610528824074852666729120665123598849369486838352320,

%F b(41) = 0,

%F b(42) = 771081103480659083177648561305159418338110532879217116850112505608,

%F b(43) = 0,

%F b(44) = 1158887466602766746036049127283646002598030062997458201209529788050000, and

%F b(n) = 1498b(n-2) + 9727b(n-4) - 3430420b(n-6) - 51780334b(n-8) + 2175631056b(n-10)

%F - 3049771912b(n-12) + 20785260864b(n-14) - 885420351008b(n-16) + 2723994857536b(n-18) + 5274700679360b(n-20)

%F + 125883661338368b(n-22) + 354089303896576b(n-24) - 880465464686592b(n-26) - 28529345908736b(n-28) + 3938132497694720b(n-30)

%F - 1757770863747072b(n-32) - 1334108047147008b(n-34) - 337906312937472b(n-36) - 49853396680704b(n-38) - 3371549327360b(n-40).

%K nonn

%O 1,1

%A _Frans J. Faase_

%E Added recurrence from Faase's web page. - _N. J. A. Sloane_, Feb 03 2009