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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. 2
 0, 9, 16, 144, 7056, 17424, 151880976, 3370896, 11141224704, 65067847056, 39037856400, 107295207555600, 189756686048400, 3749779657193648400, 2631616745340978864144, 15179712895673097530256 (list; graph; refs; listen; history; text; internal format)
 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 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; a = 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

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Last modified September 27 22:36 EDT 2020. Contains 337388 sequences. (Running on oeis4.)