A257828 Positive integers whose square is the sum of 97 consecutive squares.

679, 1545404, 3675742735, 81619738879, 194132514608060, 461744104375531831, 10253011689091642135, 24386783991798773338556, 58003955471481693294113311, 1287975802673112210113634031, 3063449905150311732357259611836, 7286414311424213782299531873117895

Offset: 1

Author

Colin Barker, May 10 2015

Keywords

• nonn
• easy

Comments

Positive integers x in the solutions to 2*x^2-194*y^2-18624*y-599072 = 0.

Examples

			679 is in the sequence because 679^2 = 461041 = 15^2+16^2+...+111^2.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..370
• Index entries for linear recurrences with constant coefficients, signature (0,0,125619266,0,0,-1).

Crossrefs

Cf. A001653, A180274, A218395, A257761, A257765, A257767, A257780, A257781, A257823-A257826, A257827.

Programs

Magma

I:=[679,1545404,3675742735,81619738879, 194132514608060,461744104375531831]; [n le 6 select I[n] else 125619266*Self(n-3)-Self(n-6): n in [1..20]]; // Vincenzo Librandi, May 11 2015

Mathematica

LinearRecurrence[{0, 0, 125619266, 0, 0, -1}, {679, 1545404, 3675742735, 81619738879, 194132514608060, 461744104375531831}, 30] (* Vincenzo Librandi, May 11 2015 *)
Rest[CoefficientList[Series[-679x(x-1)(x^4+2277x^3+5415742x^2+ 2277x+1)/ (x^6-125619266x^3+1),{x,0,15}],x]] (* Harvey P. Dale, Aug 02 2021 *)

PARI

Vec(-679*x*(x-1)*(x^4+2277*x^3+5415742*x^2+2277*x+1) / (x^6-125619266*x^3+1) + O(x^100))

Formula

a(n) = 125619266*a(n-3)-a(n-6).

G.f.: -679*x*(x-1)*(x^4+2277*x^3+5415742*x^2+2277*x+1) / (x^6-125619266*x^3+1).