cp's OEIS Frontend

A087955 a(n) is the square of the n-th partial sum minus the n-th partial sum of the squares, divided by a(n-1), for all n>=1, starting with a(0)=1, a(1)=2.

%I A087955 #5 Mar 24 2017 14:21:36
%S A087955 1,2,2,8,12,34,62,152,304,698,1458,3248,6924,15210,32734,71440,154432,
%T A087955 336018,727874,1581496,3429100,7445714,16151518,35059560,76068400,
%U A087955 165095562,358241202,777459488,1687087532,3661224794,7945027902
%N A087955 a(n) is the square of the n-th partial sum minus the n-th partial sum of the squares, divided by a(n-1), for all n>=1, starting with a(0)=1, a(1)=2.
%H A087955 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-1).
%F A087955 a(n) = a(n-1) + 3a(n-2) - a(n-3) for n>3; G.f.: (1+x-3x^2+x^3)/(1-x-3x^2+x^3).
%e A087955 a(4)=12 since ((1+2+2+8)^2 - (1^2+2^2+2^2+8^2))/8 = (13^2-73)/8 = 12.
%t A087955 LinearRecurrence[{1,3,-1},{1,2,2,8},40] (* _Harvey P. Dale_, Mar 24 2017 *)
%K A087955 nonn
%O A087955 0,2
%A A087955 _Paul D. Hanna_, Sep 16 2003