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A137882
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Number of (directed) Hamiltonian paths in the n-ladder graph.
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11
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2, 8, 16, 28, 44, 64, 88, 116, 148, 184, 224, 268, 316, 368, 424, 484, 548, 616, 688, 764, 844, 928, 1016, 1108, 1204, 1304, 1408, 1516, 1628, 1744, 1864, 1988, 2116, 2248, 2384, 2524, 2668, 2816, 2968, 3124, 3284, 3448, 3616, 3788, 3964, 4144, 4328, 4516, 4708, 4904, 5104, 5308, 5516, 5728, 5944, 6164, 6388, 6616, 6848, 7084, 7324, 7568, 7816
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OFFSET
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1,1
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LINKS
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FORMULA
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For n>2, m=p^3*q (p,q = primes), a(n) = Sum_{d|m}, (n-1)^(bigomega(d)-omega(d)) = Sum_{d|m}, (n-1)^(A001222(d)-A001221(d))). - Jaroslav Krizek, Sep 24 2009
G.f.: 2*x*(1+x-x^2+x^3)/(1-x)^3. - Colin Barker, Jan 20 2012
Sum_{n>=1} 1/a(n) = 1/4 + Pi*tanh(sqrt(7)*Pi/2)/(2*sqrt(7)). - Amiram Eldar, Dec 23 2022
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MAPLE
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MATHEMATICA
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CoefficientList[Series[2*x*(1 + x - x^2 + x^3)/(1 - x)^3, {x, 0, 50}], x] (* G. C. Greubel, Apr 25 2017 *)
LinearRecurrence[{3, -3, 1}, {2, 8, 16, 28}, 70] (* Harvey P. Dale, Nov 15 2018 *)
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PROG
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(PARI) my(x='x+O('x^50)); Vec(2*x*(1 + x - x^2 + x^3)/(1 - x)^3) \\ G. C. Greubel, Apr 25 2017
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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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Corrected the formula which was confusing offsets - R. J. Mathar, Jun 04 2010
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STATUS
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approved
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