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A087958 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.

%I A087958 #11 Apr 25 2025 01:21:46
%S A087958 1,5,2,17,18,67,104,287,532,1289,2598,5933,12438,27639,59020,129499,
%T A087958 278920,608397,1315658,2861929,6200506,13470635,29210224,63421623,
%U A087958 137581660,298636305,647959662,1406286917,3051529598,6622430687
%N A087958 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 A087958 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-1).
%F A087958 a(n) = a(n-1) + 3*a(n-2) - a(n-3) for n>3.
%F A087958 G.f.: (1+4*x-6*x^2+x^3)/(1-x-3*x^2+x^3).
%e A087958 a(4) = 18 since ((1+5+2+17)^2 - (1^2+5^2+2^2+17^2))/17 = (25^2-319)/17 = 18.
%t A087958 Join[{1},LinearRecurrence[{1,3,-1},{5,2,17},30]] (* _Harvey P. Dale_, Jul 07 2011 *)
%o A087958 (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 A087958 Cf. A087640, A087955, A087956, A087957.
%K A087958 nonn,easy
%O A087958 0,2
%A A087958 _Paul D. Hanna_, Sep 16 2003