A180259 Squares which are the sum of consecutive squares starting with 25^2.

625, 33124, 38025, 127449, 64529089, 81180100, 15884821225, 3370675683600

Offset

1,1

Comments

That is, terms are squares of the form sum_{i=25..m} i^2 = (m-24) *(2*m^2+51*m+1225) / 6 for some m. Known solutions refer to m = 25, 48, 50, 73, 578, 624, 3625 and 21624, and no further in the range m <= 70000000.

This sequence is complete. See A180442 and A184763.

Links

Table of n, a(n) for n=1..8.

Example

38025 is in the sequence because 38025 = 195^2 = 25^2 + 26^2 + ... + 50^2.

Mathematica

Select[Accumulate[Range[25, 22000]^2], IntegerQ[Sqrt[#]] &] (* Harvey P. Dale, Aug 10 2023 *)

Prog

(PARI) for(n=26, 9999999, t=n*(n+1)*(2*n+1)/6-4900; if(issquare(t), print1(t, ", ")))

Crossrefs

Cf. A001032, A094196, A151557, A180273.

Sequence in context: A017044 A080175 A017128 * A017224 A106321 A017332

Adjacent sequences: A180256 A180257 A180258 * A180260 A180261 A180262

Keyword

nonn,fini,full

Author

Zhining Yang, Jan 17 2011

Status

approved