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 A137882 Number of (directed) Hamiltonian paths in the n-ladder graph. 11
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Eric Weisstein's World of Mathematics, Hamiltonian Path Eric Weisstein's World of Mathematics, Ladder Graph Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA 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 For n>1, a(n) = 2*(n^2-n+2); first diagonal of [A154685]. - Vincenzo Librandi, Nov 24 2010 G.f.: 2*x*(1+x-x^2+x^3)/(1-x)^3. - Colin Barker, Jan 20 2012 MAPLE A137882:=n->2*(n^2-n+2): 2, seq(A137882(n), n=2..100); # Wesley Ivan Hurt, Apr 25 2017 MATHEMATICA 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 *) PROG (PARI) x='x+O('x^50); Vec(2*x*(1 + x - x^2 + x^3)/(1 - x)^3) \\ G. C. Greubel, Apr 25 2017 CROSSREFS Cf. A001221, A001222, A154685. Sequence in context: A322945 A157512 A252594 * A194643 A327329 A136514 Adjacent sequences:  A137879 A137880 A137881 * A137883 A137884 A137885 KEYWORD nonn,easy AUTHOR Eric W. Weisstein, Feb 20 2008 EXTENSIONS Extended and formula corrected by Max Alekseyev, Apr 11 2009 Corrected the formula which was confusing offsets - R. J. Mathar, Jun 04 2010 STATUS approved

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Last modified October 5 13:40 EDT 2022. Contains 357258 sequences. (Running on oeis4.)