A124356 Number of (directed) Hamiltonian cycles on the Moebius ladder graph M_n (for n >= 4).

2, 8, 6, 12, 10, 16, 14, 20, 18, 24, 22, 28, 26, 32, 30, 36, 34, 40, 38, 44, 42, 48, 46, 52, 50, 56, 54, 60, 58, 64, 62, 68, 66, 72, 70, 76, 74, 80, 78, 84, 82, 88, 86, 92, 90, 96, 94, 100, 98, 104, 102, 108, 106, 112, 110, 116, 114, 120, 118, 124, 122, 128, 126, 132

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Hamiltonian Cycle.

Eric Weisstein's World of Mathematics, Moebius Ladder.

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Formula

a(n) = 2*n if n is odd, a(n) = 2*n+4 if n is even.

a(n) = 2(n+1) + 2(-1)^n. - Paul Barry, Feb 17 2008

a(n) - a(n-4) = 8. - Paul Curtz, Apr 19 2011

a(n) = a(n-1) + a(n-2) - a(n-3). - Joerg Arndt, Apr 22 2011

G.f.: 2*x*(1+3*x-2*x^2)/((1-x)^2*(1+x)). - Colin Barker, Jan 23 2012

a(n) = 2*A014681(n+1). - R. J. Mathar, Nov 27 2015

Sum_{n>=1} (-1)^(n+1)/a(n) = log(2)/2 + 1/4. - Amiram Eldar, Feb 14 2026

Mathematica

LinearRecurrence[{1, 1, -1}, {2, 8, 6}, 100] (* Amiram Eldar, Feb 14 2026 *)

Prog

(Magma) [2*(n+1)+2*(-1)^n: n in [1..70]]; // Vincenzo Librandi, Aug 11 2011
(PARI) a(n) = 2*(n + 1 + (-1)^n); \\ Amiram Eldar, Feb 14 2026

Crossrefs

Cf. A014681.

Sequence in context: A054029 A392064 A197589 * A277249 A320262 A019186

Adjacent sequences: A124353 A124354 A124355 * A124357 A124358 A124359

Keyword

nonn,easy

Author

Eric W. Weisstein, Nov 05 2006

Status

approved