A087958 - OEIS

%I #8 Jul 31 2015 12:41:59

%S 1,5,2,17,18,67,104,287,532,1289,2598,5933,12438,27639,59020,129499,

%T 278920,608397,1315658,2861929,6200506,13470635,29210224,63421623,

%U 137581660,298636305,647959662,1406286917,3051529598,6622430687

%N 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)=5.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1, 3, -1).

%F a(n) = a(n-1) + 3a(n-2) - a(n-3) for n>3; G.f.: (1+4x-6x^2+x^3)/(1-x-3x^2+x^3).

%e a(4)=18 since ((1+5+2+17)^2 - (1^2+5^2+2^2+17^2))/17 = (25^2-217)/17 = 18.

%t Join[{1},LinearRecurrence[{1,3,-1},{5,2,17},30]] (* _Harvey P. Dale_, Jul 07 2011 *)

%o (PARI) a(0)=1; a(1)=5; for(n=2,50,a(n)=((sum(k=0,n,a(k))^2-sum(k=0,n,a(k)^2))/a(n-1))

%Y Cf. A087640, A087955, A087956, A087957.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Sep 16 2003