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A124349 Numbers of directed Hamiltonian cycles on the n-prism graph. 3
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, 130 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

LINKS

Table of n, a(n) for n=3..65.

Eric Weisstein's World of Mathematics, Hamiltonian Cycle

Eric Weisstein's World of Mathematics, Prism Graph

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

FORMULA

a(n) = 2*n + (1-(n mod 2))*4.

From Colin Barker, Aug 22 2012: (Start)

a(n) = a(n-1)+a(n-2)-a(n-3).

G.f.: 2*x^3*(3+3*x-4*x^2)/((1-x)^2*(1+x)). (End)

a(n) = 2*A014681(n+1). - R. J. Mathar, Jan 25 2016

MAPLE

seq( 2*n + (1-(n mod 2))*4, n=3..100); # Robert Israel, Mar 14 2016

MATHEMATICA

Table[2 n + (1 - Mod[n, 2]) 4, {n, 3, 100}] (* Vincenzo Librandi, Jan 26 2016 *)

PROG

(MAGMA) [2*n+(1-(n mod 2))*4: n in [3..80]]; // Vincenzo Librandi, Jan 26 2016

(PARI) Vec(2*x^3*(3+3*x-4*x^2)/((1-x)^2*(1+x)) + O(x^100)) \\ Altug Alkan, Mar 14 2016

CROSSREFS

Cf. A124350, A270273.

Sequence in context: A315777 A279606 A164378 * A315566 A236926 A134383

Adjacent sequences:  A124346 A124347 A124348 * A124350 A124351 A124352

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Oct 26 2006

EXTENSIONS

Name clarified by Andrew Howroyd, Mar 14 2016

STATUS

approved

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Last modified February 22 01:55 EST 2019. Contains 320381 sequences. (Running on oeis4.)