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

0,2

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.

Links

Table of n, a(n) for n=0..15.

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

Example

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.

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);

Crossrefs

Sequence in context: A267088 A204268 A075373 * A053911 A171522 A236287

Adjacent sequences: A072467 A072468 A072469 * A072471 A072472 A072473

Keyword

nonn

Author

Amarnath Murthy, Jun 19 2002

Extensions

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

More terms from Benoit Cloitre, Jun 21 2002

Status

approved