cp's OEIS Frontend

A087956 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)=3.

%I A087956 #8 Apr 25 2025 01:10:10
%S A087956 1,3,2,11,14,45,76,197,380,895,1838,4143,8762,19353,41496,90793,
%T A087956 195928,426811,923802,2008307,4352902,9454021,20504420,44513581,
%U A087956 96572820,209609143,454814022,987068631,2141901554,4648293425,10086929456
%N A087956 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)=3.
%F A087956 a(n) = a(n-1) + 3*a(n-2) - a(n-3) for n>3.
%F A087956 G.f.: (1+2*x-4*x^2+x^3)/(1-x-3*x^2+x^3).
%e A087956 a(4) = 14 since ((1+3+2+11)^2 - (1^2+3^2+2^2+11^2))/11 = (17^2-135)/11 = 14.
%o A087956 (PARI) a(0)=1; a(1)=3; for(n=2,50,a(n)=((sum(k=0,n,a(k))^2-sum(k=0,n,a(k)^2))/a(n-1))
%Y A087956 Cf. A087640, A087955, A087957, A087958.
%Y A087956 Essentially the same as A052973.
%K A087956 nonn,easy
%O A087956 0,2
%A A087956 _Paul D. Hanna_, Sep 16 2003