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A257708 Numbers n such that T(n) + T(n+1) + ... + T(n+24) is a square, where T = A000217 (triangular numbers). 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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).

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)).

MATHEMATICA

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

PROG

(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))

CROSSREFS

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

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

Sequence in context: A080863 A091214 A036305 * A266817 A125827 A250191

Adjacent sequences:  A257705 A257706 A257707 * A257709 A257710 A257711

KEYWORD

nonn,easy

AUTHOR

Colin Barker, May 04 2015

STATUS

approved

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Last modified February 22 15:00 EST 2020. Contains 332137 sequences. (Running on oeis4.)