A214696 Sum of next a(n) > 1 positive triangular numbers is a triangular number.

3, 7, 13, 17, 4919, 73789919

Offset

1,1

Comments

Two or more triangular numbers in the sum.

Because an oblong number is twice a triangular number, this sequence also gives: the sum of next a(n) positive oblong numbers is an oblong number.

Links

Table of n, a(n) for n=1..6.

Formula

a(n) is the smallest integer k > 1 such that (4*k^3 + 12*s*k^2 + 4*(3*s^2-1)*k)/3 + 1 is a square, where s = 1 + a(1) + a(2) + ... + a(n-1). - Max Alekseyev, Jan 30 2014

Example

1+3+6 = 10 is a triangular number, so a(1)=3, then 10+15+21+28+36+45+55 = 210 is a triangular number, seven summands, so a(2)=7.

Crossrefs

Cf. A000217, A073684, A214648.

Sequence in context: A032437 A076746 A243706 * A291661 A310256 A310257

Adjacent sequences: A214693 A214694 A214695 * A214697 A214698 A214699

Keyword

nonn,more

Author

Alex Ratushnyak, Jul 26 2012

Status

approved