A262492 The index of the first of two consecutive positive triangular numbers (A000217) the sum of which is equal to the sum of thirteen consecutive positive triangular numbers.

25, 90, 207, 1117, 2560, 9255, 21202, 114022, 261195, 944020, 2162497, 11629227, 26639430, 96280885, 220553592, 1186067232, 2716960765, 9819706350, 22494303987, 120967228537, 277103358700, 1001513766915, 2294198453182, 12337471243642, 28261825626735

Offset: 1

Author

Colin Barker, Sep 24 2015

Keywords

• nonn
• easy

Comments

For the index of the first of the corresponding thirteen consecutive triangular numbers, see A257293.

Examples

			25 is in the sequence because T(25)+T(26) = 325+351 = 676 = 6+...+120 = T(3)+...+T(15), 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 (1,0,0,102,-102,0,0,-1,1).

Crossrefs

Cf. A000217, A257293, A262489, A262490, A262491.

Programs

PARI

Vec(-x*(12*x^8+13*x^6+65*x^5-1107*x^4+910*x^3+117*x^2+65*x+25)/((x-1)*(x^4-10*x^2-1)*(x^4+10*x^2-1)) + O(x^30))

Formula

G.f.: -x*(12*x^8+13*x^6+65*x^5-1107*x^4+910*x^3+117*x^2+65*x+25) / ((x-1)*(x^4-10*x^2-1)*(x^4+10*x^2-1)).