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Number of perfect matchings in the P_6 X C_n graph.
1

%I #15 Jan 10 2018 16:03:23

%S 91,1681,2911,28561,79808,591361,2091817,13344409,53924597,315169009,

%T 1380947751,7649951296,35269184041,188926707649,899769503723,

%U 4718266032649,22943942934823,118691459382721,584955154102592,2999832755191441,14912246613880433,76049269944443041,380145205524781061

%N Number of perfect matchings in the P_6 X C_n graph.

%H S. N. Perepechko, <a href="http://www.jip.ru/2014/340-356-2014.pdf">The number of perfect matchings in one kind of strip graphs (in Russian)</a>, Information Processes, 14 (2014), 340-356.

%F G.f. x^3*(91 + 1590*x - 4048*x^2 - 69300*x^3 + 50780*x^4 + 1164101*x^5 - 138254*x^6 - 10058547*x^7 - 1562576*x^8 + 50264529*x^9 + 13812974*x^10 - 155013203*x^11 - 47809304*x^12 + 306988809*x^13 + 89155840*x^14 - 399510007*x^15 - 96791692*x^16 + 345081045*x^17 + 62203726*x^18 - 197547813*x^19 - 23125568*x^20 + 74027795*x^21 + 4550826*x^22 - 17725337*x^23 - 329540*x^24 + 2608475*x^25 - 24182*x^26 - 221705*x^27 + 4727*x^28 + 9737*x^29 - 170*x^30 - 169*x^31)/((1 - x)*(1 + x)*(1 + 3*x - 4*x^2 + x^3)*(1 + 5*x + 6*x^2 + x^3)*(1 - 4*x + 3*x^2 + x^3)*(1 - 2*x - x^2 + x^3)*(1 - x - 2*x^2 + x^3)*(1 - 3*x - 4*x^2 -x^3)*(1 - 6*x + 5*x^2 - x^3)*(1 + 4*x + 3*x^2 - x^3)*(1 + 2*x - x^2 - x^3)*(1 + x - 2*x^2 - x^3)).

%Y Cf. A068397, A102091, A252054, A253150.

%K nonn,easy

%O 3,1

%A _Sergey Perepechko_, Feb 02 2015