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 A003740 Number of spanning trees with degrees 1 and 3 in W_5 X P_2n. 1
 208, 335344, 503672968, 757005488704, 1137734095903816, 1709944335224262352, 2569941155563565968488, 3862463470575397280285088, 5805045002479537990606632936 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154. LINKS Sean A. Irvine, Table of n, a(n) for n = 1..100 F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154. F. Faase, Counting Hamiltonian cycles in product graphs F. Faase, Results from the counting program Index entries for sequences related to trees FORMULA If b(n) denotes the number of spanning trees with degrees 1 and 3 in W_5 X P_n we have: b(1) = 0, b(2) = 208, b(3) = 0, b(4) = 335344, b(5) = 0, b(6) = 503672968, b(7) = 0, b(8) = 757005488704, b(9) = 0, b(10) = 1137734095903816, b(11) = 0, b(12) = 1709944335224262352, b(13) = 0, b(14) = 2569941155563565968488, b(15) = 0, b(16) = 3862463470575397280285088, b(17) = 0, b(18) = 5805045002479537990606632936, b(19) = 0, b(20) = 8724625549856078166453269723376, b(21) = 0, b(22) = 13112575518826856642901203139743240, b(23) = 0, b(24) = 19707394403851935411114869745719526144, b(25) = 0, b(26) = 29619001517386258600018494299567252781896, b(27) = 0, b(28) = 44515537310983054901068606912734277302893072, b(29) = 0, b(30) = 66904114270101652083096747543361961556161338280, b(31) = 0, b(32) = 100552768239022085083137539569611934600600485769824, b(33) = 0, b(34) = 151124625306471850563573728012268031905685321872309416, b(35) = 0, b(36) = 227131015624872535892492790329036203871753015873169846576, b(37) = 0, b(38) = 341363944851262010688127945467040823127463725134532755058760, b(39) = 0, b(40) = 513049010606610528824074852666729120665123598849369486838352320, b(41) = 0, b(42) = 771081103480659083177648561305159418338110532879217116850112505608, b(43) = 0, b(44) = 1158887466602766746036049127283646002598030062997458201209529788050000, and b(n) = 1498b(n-2) + 9727b(n-4) - 3430420b(n-6) - 51780334b(n-8) + 2175631056b(n-10) - 3049771912b(n-12) + 20785260864b(n-14) - 885420351008b(n-16) + 2723994857536b(n-18) + 5274700679360b(n-20) + 125883661338368b(n-22) + 354089303896576b(n-24) - 880465464686592b(n-26) - 28529345908736b(n-28) + 3938132497694720b(n-30) - 1757770863747072b(n-32) - 1334108047147008b(n-34) - 337906312937472b(n-36) - 49853396680704b(n-38) - 3371549327360b(n-40). CROSSREFS Sequence in context: A184276 A268091 A209300 * A303688 A080532 A153442 Adjacent sequences: A003737 A003738 A003739 * A003741 A003742 A003743 KEYWORD nonn AUTHOR Frans J. Faase EXTENSIONS Added recurrence from Faase's web page. - N. J. A. Sloane, Feb 03 2009 STATUS approved

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