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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.
1
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.
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
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