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

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