A220864 Number of perfect matchings in the graph C_4 X C_n.

50, 272, 722, 3108, 10082, 39952, 140450, 537636, 1956242, 7379216, 27246962, 102144036, 379501250, 1418981392, 5285770562, 19742287908, 73621286642, 274848860432, 1025412242450, 3827417932836, 14282150107682, 53304783436816, 198924689265122, 742414961433636, 2770663499604050, 10340361362903312

Offset: 3

Author

N. J. A. Sloane, Dec 27 2012

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 3..1000
• S. Butler and S. Osborne, Counting tilings by taking walks, 2012.

Crossrefs

Cf. A001834.

Programs

Mathematica

CoefficientList[Series[2 (25 + 36 x - 333 x^2 - 6 x^3 + 467 x^4 - 104 x^5 - 71 x^6 + 18 x^7)/((1 - x) (1 + x) (1 - 4 x + x^2) (1 - 2 x - x^2) (1 + 2 x - x^2)), {x,0, 40}], x] (* Vincenzo Librandi, Apr 20 2014 *)

PARI

Vec( 2*x^3*(25+36*x-333*x^2-6*x^3+467*x^4-104*x^5-71*x^6+18*x^7)/((1-x)*(1+x)*(1-4*x+x^2)*(1-2*x-x^2)*(1+2*x-x^2)) +O(x^66) ) \\ Joerg Arndt, Oct 22 2013

Formula

G.f.: 2*x^3*(25+36*x-333*x^2-6*x^3+467*x^4-104*x^5-71*x^6+18*x^7)/((1-x)*(1+x)*(1-4*x+x^2)*(1-2*x-x^2)*(1+2*x-x^2)). - Sergey Perepechko, Oct 21 2013

Assuming the above o.g.f. we have, for n >= 1, a(2n+1) = 2*A001834(n)^2 = (2 + sqrt(3))^(2*n+1) + (2 - sqrt(3))^(2*n+1) - 2. - Peter Bala, Apr 19 2014

Extensions

More terms from Joerg Arndt, Oct 22 2013