|
%I #38 Jan 28 2024 04:52:16
%S 6,12,10,16,14,20,18,24,22,28,26,32,30,36,34,40,38,44,42,48,46,52,50,
%T 56,54,60,58,64,62,68,66,72,70,76,74,80,78,84,82,88,86,92,90,96,94,
%U 100,98,104,102,108,106,112,110,116,114,120,118,124,122,128,126,132,130
%N Numbers of directed Hamiltonian cycles on the n-prism graph.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HamiltonianCycle.html">Hamiltonian Cycle</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_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F a(n) = 2*n + (1-(n mod 2))*4.
%F From _Colin Barker_, Aug 22 2012: (Start)
%F a(n) = a(n-1)+a(n-2)-a(n-3).
%F G.f.: 2*x^3*(3+3*x-4*x^2)/((1-x)^2*(1+x)). (End)
%F a(n) = 2*A014681(n+1). - _R. J. Mathar_, Jan 25 2016
%F E.g.f.: 2*(2 + x)*cosh(x) + 2*x*sinh(x) - 2*(2 + x + 2*x^2). - _Stefano Spezia_, Jan 28 2024
%p seq( 2*n + (1-(n mod 2))*4, n=3..100); # _Robert Israel_, Mar 14 2016
%t Table[2 n + (1 - Mod[n, 2]) 4, {n, 3, 100}] (* _Vincenzo Librandi_, Jan 26 2016 *)
%o (Magma) [2*n+(1-(n mod 2))*4: n in [3..80]]; // _Vincenzo Librandi_, Jan 26 2016
%o (PARI) Vec(2*x^3*(3+3*x-4*x^2)/((1-x)^2*(1+x)) + O(x^100)) \\ _Altug Alkan_, Mar 14 2016
%Y Cf. A014681, A124350, A270273.
%K nonn,easy
%O 3,1
%A _Eric W. Weisstein_, Oct 26 2006
%E Name clarified by _Andrew Howroyd_, Mar 14 2016
|
