A257761 Positive integers whose square is the sum of 23 consecutive squares.

92, 138, 4278, 6532, 205252, 313398, 9847818, 15036572, 472490012, 721442058, 22669672758, 34614182212, 1087671802372, 1660759304118, 52185576841098, 79681832415452, 2503820016570332, 3823067196637578, 120131175218534838, 183427543606188292

Offset

1,1

Comments

Positive integers x in the solutions to 2*x^2-46*y^2-1012*y-7590 = 0.

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,48,0,-1).

Formula

a(n) = 48*a(n-2)-a(n-4).

G.f.: -46*x*(x-1)*(x+2)*(2*x+1) / (x^4-48*x^2+1).

Example

92 is in the sequence because 92^2 = 8464 = 7^2+8^2+...+29^2.

Mathematica

LinearRecurrence[{0, 48, 0, -1}, {92, 138, 4278, 6532}, 30] (* Vincenzo Librandi, May 11 2015 *)

Prog

(PARI) Vec(-46*x*(x-1)*(x+2)*(2*x+1)/(x^4-48*x^2+1) + O(x^100))
(Magma) I:=[92, 138, 4278, 6532]; [n le 4 select I[n] else 48*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, May 11 2015

Crossrefs

Cf. A001032, A001653, A180274, A218395, A257765, A257767, A257780, A257781, A257823-A257828.

Sequence in context: A252068 A046116 A273286 * A252067 A182266 A116215

Adjacent sequences: A257758 A257759 A257760 * A257762 A257763 A257764

Keyword

nonn,easy

Author

Colin Barker, May 07 2015

Status

approved