A257708 Numbers n such that T(n) + T(n+1) + ... + T(n+24) is a square, where T = A000217 (triangular numbers).

25, 55, 208, 382, 1273, 2287, 7480, 13390, 43657, 78103, 254512, 455278, 1483465, 2653615, 8646328, 15466462, 50394553, 90145207, 293721040, 525404830, 1711931737, 3062283823, 9977869432, 17848298158, 58155284905, 104027505175, 338953840048, 606316732942

Offset: 1

Author

Colin Barker, May 04 2015

Keywords

• nonn
• easy

Comments

Positive integers y in the solutions to 2*x^2-25*y^2-625*y-5200 = 0.

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,6,-6,-1,1).

Crossrefs

Cf. A176541, A176542, A000217, A000292, A001110, A077415.

Cf. A116476 (length 11), A257293 (length 13), A257707 (length 23), A257709 (length 27), A257710 (length 37).

Programs

Mathematica

LinearRecurrence[{1, 6, -6, -1, 1}, {25, 55, 208, 382, 1273}, 50] (* Vincenzo Librandi, May 05 2015 *)

PARI

Vec(x*(x^2+4*x+5)*(2*x^2-2*x-5)/((x-1)*(x^2-2*x-1)*(x^2+2*x-1)) + O(x^100))

Formula

G.f.: x*(x^2+4*x+5)*(2*x^2-2*x-5) / ((x-1)*(x^2-2*x-1)*(x^2+2*x-1)).