A003769 Number of perfect matchings (or domino tilings) in K_4 X P_n.

3, 16, 75, 361, 1728, 8281, 39675, 190096, 910803, 4363921, 20908800, 100180081, 479991603, 2299777936, 11018898075, 52794712441, 252954664128, 1211978608201, 5806938376875, 27822713276176, 133306628004003, 638710426743841, 3060245505715200

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

• Colin Barker, Table of n, a(n) for n = 1..1000
• 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 dominoes
• Index entries for linear recurrences with constant coefficients, signature (4,4,-1).

Crossrefs

Essentially the same as A005386. First differences of A099025.

Programs

PARI

Vec(x*(3 + 4*x - x^2) / ((1 + x)*(1 - 5*x + x^2)) + O(x^40)) \\ Colin Barker, Dec 16 2017

Formula

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

a(n) = (1/7)*(6*A030221(n) - A054477(n) + 2(-1)^n).

G.f.: x*(3+4*x-x^2)/((1+x)*(1-5*x+x^2)). - R. J. Mathar, Dec 16 2008

a(n) = 2^(-1-n)*((-1)^n*2^(2+n) + (5-sqrt(21))^(1+n) + (5+sqrt(21))^(1+n)) / 7. - Colin Barker, Dec 16 2017