A124349 Numbers of directed Hamiltonian cycles on the n-prism graph.
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
Offset: 3
Links
- 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).
Programs
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Magma
[2*n+(1-(n mod 2))*4: n in [3..80]]; // Vincenzo Librandi, Jan 26 2016
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Maple
seq( 2*n + (1-(n mod 2))*4, n=3..100); # Robert Israel, Mar 14 2016
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Mathematica
Table[2 n + (1 - Mod[n, 2]) 4, {n, 3, 100}] (* 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
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
E.g.f.: 2*(2 + x)*cosh(x) + 2*x*sinh(x) - 2*(2 + x + 2*x^2). - Stefano Spezia, Jan 28 2024
Extensions
Name clarified by Andrew Howroyd, Mar 14 2016