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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. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Eric Weisstein's World of Mathematics, Hamiltonian Path.
Eric Weisstein's World of Mathematics, Prism Graph.
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
Sequence in context: A128205 A085250 A166870 * A112611 A363092 A212066
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Oct 26 2006
EXTENSIONS
Formula and further terms from Max Alekseyev, Feb 07 2008
STATUS
approved

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Last modified February 29 13:01 EST 2024. Contains 370425 sequences. (Running on oeis4.)