

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
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OFFSET

1,6


REFERENCES

F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129154.


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), 129154.
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 28term 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(n4)  7125a(n8) + 78668a(n12)  581608a(n16) + 2138065a(n20)
 5215246a(n24) + 16969316a(n28)  43146455a(n32) + 39514076a(n36) + 7628882a(n40)
 6116529a(n44) + 23336a(n48)  2876a(n52) + 64a(n56).


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



