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A003740 Number of spanning trees with degrees 1 and 3 in W_5 X P_2n. 0
208, 335344, 503672968, 757005488704, 1137734095903816, 1709944335224262352, 2569941155563565968488, 3862463470575397280285088, 5805045002479537990606632936 (list; graph; refs; listen; history; 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

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 Hamilton cycles in product graphs

F. Faase, Results from the counting program

F. Faase, Counting Hamilton cycles in product graphs

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: A184681 A172967 A184276 * A080532 A153442 A159274

Adjacent sequences:  A003737 A003738 A003739 * A003741 A003742 A003743

KEYWORD

nonn

AUTHOR

Frans Faase (Frans_LiXia(AT)wxs.nl)

EXTENSIONS

Added recurrence from Faase's web page. - N. J. A. Sloane (njas(AT)research.att.com), Feb 03 2009

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Last modified February 13 08:12 EST 2012. Contains 205451 sequences.