A145415 Number of 2-factors in P_7 X P_2n.

8, 779, 99051, 13049563, 1729423756, 229435550806, 30443972466433, 4039769151988768, 536061241088972481, 71133264482944200277, 9439112402375129121841, 1252534193959746441955912, 166206508635573867359551206, 22054969579015463381016539631

Offset: 1

Author

N. J. A. Sloane, Feb 03 2009

Keywords

• nonn
• easy

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, Counting Hamiltonian cycles in product graphs.
• F. Faase, Results from the counting program

Programs

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

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).

Extensions

More terms from Alois P. Heinz, Mar 23 2009