A257827 Positive integers whose square is the sum of 96 consecutive squares.

652, 724, 788, 1012, 1828, 2372, 2596, 2908, 6164, 6908, 7564, 9836, 17996, 23404, 25628, 28724, 60988, 68356, 74852, 97348, 178132, 231668, 253684, 284332, 603716, 676652, 740956, 963644, 1763324, 2293276, 2511212, 2814596, 5976172, 6698164, 7334708

Offset: 1

Author

Colin Barker, May 10 2015

Keywords

• nonn
• easy

Comments

Positive integers x in the solutions to 2*x^2-192*y^2-18240*y-580640 = 0.

Examples

			652 is in the sequence because 652^2 = 425104 = 13^2+14^2+...+108^2.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,10,0,0,0,0,0,0,0,-1).

Crossrefs

Cf. A001653, A180274, A218395, A257761, A257765, A257767, A257780, A257781, A257823-A257826, A257828.

Programs

Magma

I:=[652,724,788,1012,1828,2372,2596,2908,6164,6908, 7564,9836,17996,23404,25628,28724]; [n le 16 select I[n] else 10*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, May 11 2015

Mathematica

LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, -1}, {652, 724, 788, 1012, 1828, 2372, 2596, 2908, 6164, 6908, 7564, 9836, 17996, 23404, 25628, 28724}, 40] (* Vincenzo Librandi, May 11 2015 *)

PARI

Vec(-4*x*(89*x^15 +83*x^14 +79*x^13 +71*x^12 +71*x^11 +79*x^10 +83*x^9 +89*x^8 -727*x^7 -649*x^6 -593*x^5 -457*x^4 -253*x^3 -197*x^2 -181*x -163) / (x^16-10*x^8+1) + O(x^100))

Formula

a(n) = 10*a(n-8) -a(n-16).

G.f.: -4*x*(89*x^15 +83*x^14 +79*x^13 +71*x^12 +71*x^11 +79*x^10 +83*x^9 +89*x^8 -727*x^7 -649*x^6 -593*x^5 -457*x^4 -253*x^3 -197*x^2 -181*x-163) / (x^16 -10*x^8 +1).