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

3,1

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.

Index entries for linear recurrences with constant coefficients, signature (6,41,-234,-541,2784,3355,-14790,-11039,39210,20023,-53952,-20023,39210,11039,-14790,-3355,2784,541,-234,-41,6,1).

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)).

Mathematica

CoefficientList[Series[ 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)), {x, 0, 24}], x] (* Stefano Spezia, Apr 04 2026 *)

Crossrefs

Row n=3 of A341741.

Cf. A220864, A231087, A231485.

Sequence in context: A015048 A229589 A341048 * A032802 A224431 A280858

Adjacent sequences: A232801 A232802 A232803 * A232805 A232806 A232807

Keyword

nonn,easy

Author

Sergey Perepechko, Nov 30 2013

Status

approved