A257707 Numbers n such that T(n) + T(n+1) + ... + T(n+22) is a square, where T = A000217 (triangular numbers).

56, 470, 1094, 7856, 128534, 201539, 3293081, 23435699, 53805155, 382911281, 6256309475, 9809462822, 160274811896, 1140616029542, 2618697452438, 18636292598096, 304494582579398, 477426555904883, 7800575092244921, 55513782134933123, 127452004956911987

Offset: 1

Author

Colin Barker, May 04 2015

Keywords

• nonn
• easy

Comments

Positive integers y in the solutions to 2*x^2-23*y^2-529*y-4048 = 0.

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,48670,-48670,0,0,0,0,-1,1).

Crossrefs

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

Cf. A116476 (length 11), A257293 (length 13), A257708 (length 25), A257709 (length 27), A257710 (length 37).

Programs

Mathematica

LinearRecurrence[{1, 0, 0, 0, 0, 48670, -48670, 0, 0, 0, 0, -1, 1}, {56, 470, 1094, 7856, 128534, 201539, 3293081, 23435699, 53805155, 382911281, 6256309475, 9809462822, 160274811896}, 50] (* Vincenzo Librandi, May 05 2015 *)

PARI

Vec(x*(10*x^12 +3*x^11 +66*x^10 +414*x^9 +624*x^8 +6762*x^7 -366022*x^6 -73005*x^5 -120678*x^4 -6762*x^3 -624*x^2 -414*x -56) / ((x -1)*(x^12 -48670*x^6 +1)) + O(x^100))

Formula

G.f.: x*(10*x^12 +3*x^11 +66*x^10 +414*x^9 +624*x^8 +6762*x^7 -366022*x^6 -73005*x^5 -120678*x^4 -6762*x^3 -624*x^2 -414*x -56) / ((x -1)*(x^12 -48670*x^6 +1)).