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A262489 The index of the first of two consecutive positive triangular numbers (A000217) the sum of which is equal to the sum of three consecutive positive triangular numbers. 4
7, 18, 78, 187, 781, 1860, 7740, 18421, 76627, 182358, 758538, 1805167, 7508761, 17869320, 74329080, 176888041, 735782047, 1751011098, 7283491398, 17333222947, 72099131941, 171581218380, 713707828020, 1698478960861, 7064979148267, 16813208390238 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For the index of the first of the corresponding three consecutive triangular numbers, see A165517.

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,10,-10,-1,1).

FORMULA

a(n) = a(n-1)+10*a(n-2)-10*a(n-3)-a(n-4)+a(n-5) for n>5.

G.f.: -x*(x^4-x^3-10*x^2+11*x+7) / ((x-1)*(x^4-10*x^2+1)).

EXAMPLE

7 is in the sequence because T(7)+T(8) = 28+36 = 64 = 15+21+28 = T(5)+T(6)+T(7), where T(k) is the k-th triangular number.

PROG

(PARI) Vec(-x*(x^4-x^3-10*x^2+11*x+7)/((x-1)*(x^4-10*x^2+1)) + O(x^30))

CROSSREFS

Cf. A000217, A165517, A262490, A262491, A262492.

Sequence in context: A223240 A019534 A024830 * A030982 A203381 A207158

Adjacent sequences:  A262486 A262487 A262488 * A262490 A262491 A262492

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Sep 24 2015

STATUS

approved

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Last modified December 16 01:36 EST 2017. Contains 296063 sequences.