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
Alois P. Heinz, Table of n, a(n) for n = 1..470
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, Results from the counting program
FORMULA
Recurrence: If b(n) denotes the number of 2-factors in P_7 X P_n then we have
b(1) = 0,
b(2) = 8,
b(3) = 0,
b(4) = 779,
b(5) = 0,
b(6) = 99051,
b(7) = 0,
b(8) = 13049563,
b(9) = 0,
b(10) = 1729423756,
b(11) = 0,
b(12) = 229435550806,
b(13) = 0,
b(14) = 30443972466433,
b(15) = 0,
b(16) = 4039769151988768,
b(17) = 0,
b(18) = 536061241088972481, and
b(n) = 171b(n-2) - 5496b(n-4) + 56617b(n-6) - 240021b(n-8) + 457923b(n-10)
- 420254b(n-12) + 186912b(n-14) - 37569b(n-16) + 2584b(n-18).
MAPLE
a:= n-> (Matrix([[4039769151988768, 30443972466433, 229435550806, 1729423756, 13049563, 99051, 779, 8, 14/19]]). Matrix(9, (i, j)-> if i=j-1 then 1 elif j=1 then [171, -5496, 56617, -240021, 457923, -420254, 186912, -37569, 2584][i] else 0 fi)^n)[1, 9]: seq(a(n), n=1..20); # Alois P. Heinz, Mar 23 2009
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Feb 03 2009
EXTENSIONS
More terms from Alois P. Heinz, Mar 23 2009
STATUS
approved