A152298 - OEIS

%I #13 Jun 19 2015 11:19:42

%S 0,1,1,13,10,121,91,1093,820,9841,7381,88573,66430,797161,597871,

%T 7174453,5380840,64570081,48427561,581130733,435848050,5230176601,

%U 3922632451,47071589413,35303692060,423644304721,317733228541,3812798742493,2859599056870

%N a(n) = (3^n-1)/2 if n odd, (3^n-1)/8 if n even.

%H Vincenzo Librandi, <a href="/A152298/b152298.txt">Table of n, a(n) for n = 0..300</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,10,0,-9).

%F a(n) = (3^n - 1)/(2^(3 - 2*Mod[n, 2])).

%F a(n) = 10*a(n-2) - 9*a(n-4). - _Colin Barker_, Jun 17 2015

%F G.f.: x*(3*x^2+x+1) / ((x-1)*(x+1)*(3*x-1)*(3*x+1)). - _Colin Barker_, Jun 17 2015

%t Clear[a, n];

%t a[n_] := (3^n - 1)/(2^(3 - 2*Mod[n, 2]));

%t Table[a[n], {n, 0, 30}]

%o (PARI) concat(0, Vec(x*(3*x^2+x+1)/((x-1)*(x+1)*(3*x-1)*(3*x+1)) + O(x^100))) \\ _Colin Barker_, Jun 17 2015

%Y Cf. A003462.

%K nonn,easy

%O 0,4

%A _Roger L. Bagula_, Dec 02 2008

%E Edited by _N. J. A. Sloane_, Aug 15 2013