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REFERENCES
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F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.
Per Hakan Lundow, "Computation of matching polynomials and the number of 1-factors in polygraphs", Research report, No 12, 1996, Department of Math., Umea University, Sweden.
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LINKS
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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 Hamilton cycles in product graphs
F. Faase, Results from the counting program
Per Hakan Lundow, Enumeration of matchings in polygraphs, 1998.
James A. Sellers, Domino Tilings and Products of Fibonacci and Pell Numbers, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.2
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FORMULA
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Recurrence from Faase web site: a(1) = 1,
a(2) = 34,
a(3) = 153,
a(4) = 2245,
a(5) = 14824,
a(6) = 167089,
a(7) = 1292697,
a(8) = 12988816,
a(9) = 108435745,
a(10) = 1031151241,
a(11) = 8940739824,
a(12) = 82741005829,
a(13) = 731164253833,
a(14) = 6675498237130,
a(15) = 59554200469113,
a(16) = 540061286536921,
a(17) = 4841110033666048,
a(18) = 43752732573098281,
a(19) = 393139145126822985,
a(20) = 3547073578562247994,
a(21) = 31910388243436817641,
a(22) = 287665106926232833093,
a(23) = 2589464895903294456096,
a(24) = 23333526083922816720025,
a(25) = 210103825878043857266833,
a(26) = 1892830605678515060701072,
a(27) = 17046328120997609883612969,
a(28) = 153554399246902845860302369,
a(29) = 1382974514097522648618420280,
a(30) = 12457255314954679645007780869,
a(31) = 112199448394764215277422176953,
a(32) = 1010618564986361239515088848178, and
a(n) = 153a(n-2) - 7480a(n-4) + 151623a(n-6) - 1552087a(n-8) + 8933976a(n-10)
- 30536233a(n-12) + 63544113a(n-14) - 81114784a(n-16) + 63544113a(n-18) - 30536233a(n-20)
+ 8933976a(n-22) - 1552087a(n-24) + 151623a(n-26) - 7480a(n-28) + 153a(n-30) - a(n-32).
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