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A028470
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Number of perfect matchings in graph P_{8} X P_{n}.
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5
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1, 34, 153, 2245, 14824, 167089, 1292697, 12988816, 108435745, 1031151241, 8940739824, 82741005829, 731164253833, 6675498237130, 59554200469113, 540061286536921, 4841110033666048, 43752732573098281
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| 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
| 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
| 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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MAPLE
| a:= n-> (Matrix(16, (i, j)-> `if` (i=j-1, 1, `if` (i=16, [-1, 1, 76, 69, -921, -584, 4019, 829, -7012][min(j, 18-j)], 0)))^n. <<seq([1292697, 167089, 14824, 2245, 153, 34, 1, 1, 0][min(k, 18-k)], k=1..16)>>)[10, 1]: seq (a(n), n=1..50); # Alois P. Heinz, Apr 14 2011
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CROSSREFS
| Row 8 of array A099390.
Sequence in context: A159744 A192398 A167241 * A190607 A191593 A063652
Adjacent sequences: A028467 A028468 A028469 * A028471 A028472 A028473
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KEYWORD
| nonn
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AUTHOR
| Per Hakan Lundow (phl(AT)theophys.kth.se)
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EXTENSIONS
| Added recurrence from Faase's web page. - N. J. A. Sloane (njas(AT)research.att.com), Feb 03 2009
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