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

Author

Colin Barker, May 05 2015

Keywords

• nonn
• easy

Examples

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

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).

Crossrefs

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

Programs

Mathematica

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

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))

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