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A072470 a(0) = 0, a(1) = 9; for n > 1 a(n) = smallest positive square (possibly required to be greater than a(n-1)?) such that a(0) + a(1) + ... + a(n) is a square.

%I A072470 #17 Dec 14 2018 20:04:35
%S A072470 0,9,16,144,7056,17424,151880976,3370896,11141224704,65067847056,
%T A072470 39037856400,107295207555600,189756686048400,3749779657193648400,
%U A072470 2631616745340978864144,15179712895673097530256
%N A072470 a(0) = 0, a(1) = 9; for n > 1 a(n) = smallest positive square (possibly required to be greater than a(n-1)?) such that a(0) + a(1) + ... + a(n) is a square.
%C A072470 Sequence is infinite as every partial sum (n>0) is odd, say 2k + 1 and then k^2 is a candidate for the next term.
%F A072470 a(n) = A018930(n)^2. - _Benoit Cloitre_, Jun 21 2002
%F A072470 a(n) = A018929(n+1) - A018929(n) for n > 1. - _César Aguilera_, Nov 10 2018
%e A072470 a(3) = 16 as a(1) + a(2) + a(3) = 25 is also a square.
%e A072470 a(4) = 144 as 0 + 9 + 16 + 144 = 169 is also a square.
%t A072470 a[0] = 0; a[1] = 9; a[n_] := a[n] = (k = Sqrt[a[n - 1]] + 1; s = Sum[a[i], {i, 0, n - 1}]; While[ !IntegerQ[ Sqrt[s + k^2]], k++ ]; k^2);
%K A072470 nonn
%O A072470 0,2
%A A072470 _Amarnath Murthy_, Jun 19 2002
%E A072470 Edited by _N. J. A. Sloane_ and _Robert G. Wilson v_, Jun 21 2002
%E A072470 More terms from _Benoit Cloitre_, Jun 21 2002