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

1,1

Comments

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

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).

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)).

Example

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.

Prog

(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))

Crossrefs

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

Sequence in context: A087240 A044212 A044593 * A280297 A090659 A010013

Adjacent sequences: A262489 A262490 A262491 * A262493 A262494 A262495

Keyword

nonn,easy

Author

Colin Barker, Sep 24 2015

Status

approved