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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Oct 26 2006
EXTENSIONS
Formula and further terms from Max Alekseyev, Feb 07 2008
STATUS
approved