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A137882 Number of (directed) Hamiltonian paths in the n-ladder graph. 9
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 *)

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: A225289 A157512 A252594 * A194643 A136514 A077071

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 May 29 16:53 EDT 2017. Contains 287252 sequences.