A003693 Number of 2-factors in P_4 X P_n.

0, 2, 3, 18, 54, 222, 779, 2953, 10771, 40043, 147462, 545603, 2013994, 7442927, 27490263, 101563680, 375176968, 1386004383, 5120092320, 18914660608, 69873991466, 258127586367, 953569519203, 3522660270539

Offset: 1

Author

Frans J. Faase

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

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• 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 linear recurrences with constant coefficients, signature (2, 7, -2, -3, 1).

Crossrefs

Cf. A003776, A145400, A145415, A145417, A222202, A222203.

Programs

Mathematica

LinearRecurrence[{2, 7, -2, -3, 1}, {0, 2, 3, 18, 54}, 30] (* Jean-François Alcover, Sep 21 2019 *)

Formula

a(n) = 2a(n-1) + 7a(n-2) - 2a(n-3) - 3a(n-4) + a(n-5), n > 5.

G.f.: (-x*(x-1)*(x-2)*(x+1))/(-1 + x^5 - 3*x^4 - 2*x^3 + 7*x^2 + 2*x). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 10 2009