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A257711

Triangular numbers (A000217) that are the sum of seven consecutive triangular numbers.

210, 3486, 51681, 883785, 13125126, 224476266, 3333728685, 57016086141, 846753959226, 14481861401910, 215072171913081, 3678335779997361, 54627484911961710, 934282806257926146, 13875166095466359621, 237304154453733242085, 3524237560763543380386

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OFFSET

1,1

LINKS

Colin Barker, Table of n, a(n) for n = 1..830

Index entries for linear recurrences with constant coefficients, signature (1,254,-254,-1,1).

FORMULA

G.f.: -21*x*(x^4-245*x^2+156*x+10) / ((x-1)*(x^2-16*x+1)*(x^2+16*x+1)).

16*a(n) = 104 +225*A157456(n+1) +7*(-1)^n*A159678(n+1). - R. J. Mathar, Apr 28 2020

EXAMPLE

210 is in the sequence because T(20) = 210 = 10+15+21+28+36+45+55 = T(4)+ ... +T(10).

MATHEMATICA

LinearRecurrence[{1, 254, -254, -1, 1}, {210, 3486, 51681, 883785, 13125126}, 30] (* Vincenzo Librandi, Jun 27 2015 *)

PROG

(PARI) Vec(-21*x*(x^4-245*x^2+156*x+10) / ((x-1)*(x^2-16*x+1)*(x^2+16*x+1)) + O(x^100))

CROSSREFS

Cf. A000217, A001110, A129803, A131557, A257712, A257713, A259413, A259414, A259415.

Sequence in context: A024449 A235240 A103604 * A061133 A087977 A185042

Adjacent sequences: A257708 A257709 A257710 * A257712 A257713 A257714

KEYWORD

nonn,easy

AUTHOR

Colin Barker, May 05 2015

STATUS

approved

URL: https://oeis.org/A257711

⇱ A257711 - OEIS