A257765 Positive integers whose square is the sum of 26 consecutive squares.

195, 1599, 2379, 19695, 163059, 242619, 2008695, 16630419, 24744759, 204867195, 1696139679, 2523722799, 20894445195, 172989616839, 257394980739, 2131028542695, 17643244777899, 26251764312579, 217344016909695, 1799437977728859, 2677422564902319

Offset

1,1

Comments

Positive integers x in the solutions to 2*x^2-52*y^2-1300*y-11050 = 0.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,102,0,0,-1).

Formula

a(n) = 102*a(n-3)-a(n-6).

G.f.: -39*x*(x^5+x^4+5*x^3-61*x^2-41*x-5) / (x^6-102*x^3+1).

Example

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

Mathematica

LinearRecurrence[{0, 0, 102, 0, 0, -1}, {195, 1599, 2379, 19695, 163059, 242619}, 30] (* Vincenzo Librandi, May 11 2015 *)
Select[Sqrt[#]&/@Total/@Partition[Range[10^6]^2, 26, 1], IntegerQ] (* The program generates the first 7 terms of the sequence. *) (* Harvey P. Dale, Mar 10 2024 *)

Prog

(PARI) Vec(-39*x*(x^5+x^4+5*x^3-61*x^2-41*x-5) / (x^6-102*x^3+1) + O(x^100))
(Magma) I:=[195, 1599, 2379, 19695, 163059, 242619 ]; [n le 6 select I[n] else 102*Self(n-3)-Self(n-6): n in [1..30]]; // Vincenzo Librandi, May 11 2015

Crossrefs

Cf. A001032, A001653, A180274, A218395, A257761, A257767, A257780, A257781, A257823-A257828.

Sequence in context: A225713 A172354 A295130 * A259694 A066232 A284960

Adjacent sequences: A257762 A257763 A257764 * A257766 A257767 A257768

Keyword

nonn,easy

Author

Colin Barker, May 07 2015

Status

approved