cp's OEIS Frontend

A087957 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)=4.

%I A087957 #7 Apr 25 2025 01:21:50
%S A087957 1,4,2,14,16,56,90,242,456,1092,2218,5038,10600,23496,50258,110146,
%T A087957 237424,517604,1119730,2435118,5276704,11462328,24857322,53967602,
%U A087957 117077240,254122724,551386842,1196677774,2596715576,5635362056
%N A087957 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)=4.
%F A087957 a(n) = a(n-1) + 3*a(n-2) - a(n-3) for n>3.
%F A087957 G.f.: (1+3*x-5*x^2+x^3)/(1-x-3*x^2+x^3).
%e A087957 a(4) = 16 since ((1+4+2+14)^2 - (1^2+4^2+2^2+14^2))/14 = (21^2-217)/14 = 16.
%o A087957 (PARI) a(0)=1; a(1)=4; for(n=2,50,a(n)=((sum(k=0,n,a(k))^2-sum(k=0,n,a(k)^2))/a(n-1))
%Y A087957 Cf. A087640, A087955, A087956, A087958.
%K A087957 nonn,easy
%O A087957 0,2
%A A087957 _Paul D. Hanna_, Sep 16 2003