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A003780 Number of spanning trees with degrees 1 and 3 in P_5 X P_n. 0
0, 0, 0, 0, 0, 296, 0, 0, 0, 70420, 0, 0, 0, 16391166, 0, 0, 0, 3816021084, 0, 0, 0, 888375830566, 0, 0, 0, 206814474641944, 0, 0, 0, 48146529005876746, 0, 0, 0, 11208539472498838244, 0, 0, 0, 2609354391828066201746, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

REFERENCES

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

LINKS

Table of n, a(n) for n=1..41.

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

Faase gives a 28-term linear recurrence on his web page:

a(1) = 0,

a(2) = 0,

a(3) = 0,

a(4) = 0,

a(5) = 0,

a(6) = 296,

a(7) = 0,

a(8) = 0,

a(9) = 0,

a(10) = 70420,

a(11) = 0,

a(12) = 0,

a(13) = 0,

a(14) = 16391166,

a(15) = 0,

a(16) = 0,

a(17) = 0,

a(18) = 3816021084,

a(19) = 0,

a(20) = 0,

a(21) = 0,

a(22) = 888375830566,

a(23) = 0,

a(24) = 0,

a(25) = 0,

a(26) = 206814474641944,

a(27) = 0,

a(28) = 0,

a(29) = 0,

a(30) = 48146529005876746,

a(31) = 0,

a(32) = 0,

a(33) = 0,

a(34) = 11208539472498838244,

a(35) = 0,

a(36) = 0,

a(37) = 0,

a(38) = 2609354391828066201746,

a(39) = 0,

a(40) = 0,

a(41) = 0,

a(42) = 607459192887167645884388,

a(43) = 0,

a(44) = 0,

a(45) = 0,

a(46) = 141416847085185500394182672,

a(47) = 0,

a(48) = 0,

a(49) = 0,

a(50) = 32921922778799648796216249818,

a(51) = 0,

a(52) = 0,

a(53) = 0,

a(54) = 7664242427921761934124201980862,

a(55) = 0,

a(56) = 0,

a(57) = 0,

a(58) = 1784240015038927382237215443432910 and

a(n) = 262a(n-4) - 7125a(n-8) + 78668a(n-12) - 581608a(n-16) + 2138065a(n-20)

- 5215246a(n-24) + 16969316a(n-28) - 43146455a(n-32) + 39514076a(n-36) + 7628882a(n-40)

- 6116529a(n-44) + 23336a(n-48) - 2876a(n-52) + 64a(n-56).

CROSSREFS

Sequence in context: A279052 A237803 A238512 * A206339 A107924 A224170

Adjacent sequences:  A003777 A003778 A003779 * A003781 A003782 A003783

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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Last modified December 8 17:36 EST 2019. Contains 329865 sequences. (Running on oeis4.)