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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. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 9 01:35 EDT 2020. Contains 336310 sequences. (Running on oeis4.)