A257780 Positive integers whose square is the sum of 47 consecutive squares.

3854, 5170, 369890, 496226, 35505586, 47632526, 3408166366, 4572226270, 327148465550, 438886089394, 31402844526434, 42128492355554, 3014345926072114, 4043896380043790, 289345806058396510, 388171923991848286, 27774183035679992846, 37260460806837391666

Offset: 1

Author

Colin Barker, May 08 2015

Keywords

• nonn
• easy

Comments

Positive integers x in the solutions to 2*x^2-94*y^2-4324*y-67022 = 0.

Examples

			3854 is in the sequence because 3854^2 = 14853316 = 539^2+540^2+...+585^2.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0,96,0,-1).

Crossrefs

Cf. A001653, A180274, A218395, A257761, A257765, A257767, A257781, A257823-A257828.

Programs

Magma

I:=[3854,5170,369890,496226 ]; [n le 4 select I[n] else 96*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, May 11 2015

Mathematica

LinearRecurrence[{0, 96, 0, -1}, {3854, 5170, 369890, 496226}, 50] (* Vincenzo Librandi, May 11 2015 *)

PARI

Vec(-94*x*(x^3+x^2-55*x-41) / (x^4-96*x^2+1) + O(x^100))

Formula

a(n) = 96*a(n-2)-a(n-4).

G.f.: -94*x*(x^3+x^2-55*x-41) / (x^4-96*x^2+1).