A232804 Number of perfect matchings in the graph C_6 x C_n.

224, 3108, 9922, 90176, 401998, 3113860, 16091936, 114557000, 643041038, 4357599552, 25689719122, 169094614280, 1026275640544, 6640849944580, 40998347400722, 262671237617216, 1637828186763038, 10433179552323108, 65428999765032736, 415409841636546440, 2613799160004664798, 16563343174199239744

Offset: 3

Author

Sergey Perepechko, Nov 30 2013

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 3..500
• P. W. Kasteleyn, The Statistics of Dimers on a Lattice, Physica, 27 (1961), 1209-1225.

Crossrefs

Row n=3 of A341741.

Cf. A220864, A231087, A231485.

Formula

G.f: 2*x^3*(112+882*x-8955*x^2-22184*x^3+151298*x^4+192108*x^5-1004174*x^6-773678*x^7+3077791*x^8+1598624*x^9-4646368*x^10-1738444*x^11+3589216*x^12+ 1010882*x^13-1408253*x^14-318388*x^15+271982*x^16+52648*x^17-23250*x^18-4062*x^19+601*x^20+100*x^21)/((1-x)*(1+x)*(1+5*x+x^2)*(1-5*x+x^2)*(1-2*x-x^2)* (1+2*x-x^2)*(1+x-x^2)*(1-x-x^2)*(1-5*x^2+x^4)*(1-6*x-3*x^2+6*x^3+x^4)).