A124350 a(n) = 4*n*(floor(n^2/2)+1). For n >= 3, this is the number of directed Hamiltonian paths on the n-prism graph.

0, 4, 24, 60, 144, 260, 456, 700, 1056, 1476, 2040, 2684, 3504, 4420, 5544, 6780, 8256, 9860, 11736, 13756, 16080, 18564, 21384, 24380, 27744, 31300, 35256, 39420, 44016, 48836, 54120, 59644, 65664, 71940, 78744, 85820, 93456, 101380, 109896, 118716

Offset

0,2

Links

Stefano Spezia, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Hamiltonian Path.

Eric Weisstein's World of Mathematics, Prism Graph.

Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

Formula

From Colin Barker, Sep 06 2013: (Start)

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

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

a(n) = 4*n*A080827(n). - R. J. Mathar, Jan 25 2016

E.g.f.: 2*x*((2 + 3*x + x^2)*cosh(x) + (3 + 3*x + x^2)*sinh(x)). - Stefano Spezia, Jan 27 2024

Mathematica

LinearRecurrence[{2, 1, -4, 1, 2, -1}, {0, 4, 24, 60, 144, 260}, 60] (* Vincenzo Librandi, Jan 26 2016 *)

Prog

(PARI) Vec(4*x*(x^2+1)*(x^2+4*x+1)/((x-1)^4*(x+1)^2) + O(x^100)) \\ Colin Barker, Sep 06 2013

Crossrefs

Cf. A080827, A124349.

Sequence in context: A128205 A085250 A166870 * A112611 A363092 A212066

Adjacent sequences: A124347 A124348 A124349 * A124351 A124352 A124353

Keyword

nonn,easy

Author

Eric W. Weisstein, Oct 26 2006

Extensions

Formula and further terms from Max Alekseyev, Feb 07 2008

Status

approved