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

Author

Colin Barker, May 07 2015

Keywords

• nonn
• easy

Comments

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

Examples

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

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).

Crossrefs

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

Programs

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

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 *)

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))

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).