A262491 The index of the first of two consecutive positive triangular numbers (A000217) the sum of which is equal to the sum of eleven consecutive positive triangular numbers.

43, 120, 549, 3783, 17214, 47629, 216688, 1490884, 6782665, 18766098, 85374915, 587404905, 2672353188, 7393795375, 33637500214, 231436042078, 1052900373799, 2913136612044, 13253089709793, 91185213174219, 414840074924010, 1147768431350353, 5221683708158620

Offset: 1

Author

Colin Barker, Sep 24 2015

Keywords

• nonn
• easy

Comments

For the index of the first of the corresponding eleven consecutive triangular numbers, see A116476.

Examples

			43 is in the sequence because T(43)+T(44) = 946+990 = 1936 = 91+...+276 = T(13)+...+T(23), where T(k) is the k-th triangular number.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,394,-394,0,0,-1,1).

Crossrefs

Cf. A000217, A116476, A262489, A262490, A262492.

Programs

Mathematica

LinearRecurrence[{1,0,0,394,-394,0,0,-1,1},{43,120,549,3783,17214,47629,216688,1490884,6782665},30] (* Harvey P. Dale, May 17 2020 *)

PARI

Vec(-x*(10*x^8+33*x^6+77*x^5-3511*x^4+3234*x^3+429*x^2+77*x+43)/((x-1)*(x^8-394*x^4+1)) + O(x^30))

Formula

G.f.: -x*(10*x^8+33*x^6+77*x^5-3511*x^4+3234*x^3+429*x^2+77*x+43) / ((x-1)*(x^8-394*x^4+1)).