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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. 2

%I

%S 0,4,24,60,144,260,456,700,1056,1476,2040,2684,3504,4420,5544,6780,

%T 8256,9860,11736,13756,16080,18564,21384,24380,27744,31300,35256,

%U 39420,44016,48836,54120,59644,65664,71940,78744,85820,93456,101380,109896,118716

%N 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.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HamiltonianPath.html">Hamiltonian Path</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrismGraph.html">Prism Graph</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).

%F 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). - _Colin Barker_, Sep 06 2013

%F a(n) = 4*n*A080827(n). - _R. J. Mathar_, Jan 25 2016

%t LinearRecurrence[{2, 1, -4, 1, 2, -1}, {0, 4, 24, 60, 144, 260}, 60] (* _Vincenzo Librandi_, Jan 26 2016 *)

%o (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

%Y Cf. A124349.

%K nonn,easy

%O 0,2

%A _Eric W. Weisstein_, Oct 26 2006

%E Formula and further terms from _Max Alekseyev_, Feb 07 2008

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Last modified April 18 16:45 EDT 2019. Contains 322209 sequences. (Running on oeis4.)