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A003772
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Number of Hamiltonian paths in K_4 X P_n.
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1
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12, 408, 6648, 90672, 1103088, 12509256, 135409896, 1419480288, 14545113696, 146607233784, 1460033574744, 14411647534224, 141321405768144, 1379055205227432, 13408489143753672, 130019327919243840, 1258252792162873152, 12158637295940721240
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OFFSET
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1,1
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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.
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LINKS
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FORMULA
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Faase gives a 6-term linear recurrence on his web page:
a(1) = 12,
a(2) = 408,
a(3) = 6648,
a(4) = 90672,
a(5) = 1103088,
a(6) = 12509256,
a(7) = 135409896 and
a(n) = 23a(n-1) - 173a(n-2) + 421a(n-3) + 62a(n-4) - 132a(n-5) + 24a(n-6).
G.f.: 12*x*(24*x^6-164*x^5+398*x^4-275*x^3+55*x^2-11*x-1)/((2*x^2-7*x+1)^2*(6*x^2+9*x-1)). [Colin Barker, Aug 30 2012]
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MATHEMATICA
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CoefficientList[Series[12(24 x^6 - 164 x^5 + 398 x^4 - 275 x^3 + 55 x^2 - 11 x - 1)/((2 x^2 - 7 x + 1)^2 (6 x^2 + 9 x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 14 2013 *)
LinearRecurrence[{23, -173, 421, 62, -132, 24}, {12, 408, 6648, 90672, 1103088, 12509256, 135409896}, 20] (* Harvey P. Dale, Jun 11 2019 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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