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.

0, 9, 16, 144, 7056, 17424, 151880976, 3370896, 11141224704, 65067847056, 39037856400, 107295207555600, 189756686048400, 3749779657193648400, 2631616745340978864144, 15179712895673097530256

Offset: 0

Author

Amarnath Murthy, Jun 19 2002

Keywords

• nonn

Comments

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.

Examples

			a(3) = 16 as a(1) + a(2) + a(3) = 25 is also a square.
a(4) = 144 as 0 + 9 + 16 + 144 = 169 is also a square.
		

Programs

Mathematica

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);

Formula

a(n) = A018930(n)^2. - Benoit Cloitre, Jun 21 2002

a(n) = A018929(n+1) - A018929(n) for n > 1. - César Aguilera, Nov 10 2018

Extensions

Edited by N. J. A. Sloane and Robert G. Wilson v, Jun 21 2002

More terms from Benoit Cloitre, Jun 21 2002