A003734 Number of spanning trees with degrees 1 and 3 in C_5 X P_2n.

0, 260, 27420, 2504560, 223723080, 19923617840, 1773563554900, 157870122686600, 14052371971981100, 1250831588811052320, 111339169110472830220, 9910535055491682625400, 882157695038695625086700, 78522722964255506997330800, 6989473714324564174042717340

Offset

1,2

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..15.

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 12-term linear recurrence on his web page:

If b(n) denotes the number of spanning trees with degrees 1 and 3 in C_5 X P_n we have:

b(1) = 0,

b(2) = 0,

b(3) = 0,

b(4) = 260,

b(5) = 0,

b(6) = 27420,

b(7) = 0,

b(8) = 2504560,

b(9) = 0,

b(10) = 223723080,

b(11) = 0,

b(12) = 19923617840,

b(13) = 0,

b(14) = 1773563554900,

b(15) = 0,

b(16) = 157870122686600,

b(17) = 0,

b(18) = 14052371971981100,

b(19) = 0,

b(20) = 1250831588811052320,

b(21) = 0,

b(22) = 111339169110472830220,

b(23) = 0,

b(24) = 9910535055491682625400,

b(25) = 0,

b(26) = 882157695038695625086700, and

b(n) = 98b(n-2) - 745b(n-4) - 4916b(n-6) - 234b(n-8) + 160624b(n-10)

- 26648b(n-12) + 338976b(n-14) - 1265216b(n-16) - 2291392b(n-18) - 1695488b(n-20)

- 307200b(n-22) + 32768b(n-24).

Crossrefs

Sequence in context: A168187 A067639 A264162 * A216940 A200578 A200808

Adjacent sequences: A003731 A003732 A003733 * A003735 A003736 A003737

Keyword

nonn

Author

Frans J. Faase

Extensions

Added recurrence from Faase's web page. - N. J. A. Sloane, Feb 03 2009

More terms from Sean A. Irvine, Jul 29 2015

Status

approved