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.

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

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: A304142 A019534 A024830 * A030982 A203381 A207158

Adjacent sequences: A262486 A262487 A262488 * A262490 A262491 A262492

Keyword

nonn,easy

Author

Colin Barker, Sep 24 2015

Status

approved