0,2

The product of three consecutive triangular numbers with middle term A000217(m) where m is in this sequence is a square.

n is in this sequence just in case the triangle with sides 3,n,n+1 has integer area. Equivalently, n such that 2*(n+2)*(n-1) is a square. [From James Buddenhagen (jbuddenh(AT)gmail.com), Oct 19 2008]

Triangular numbers that are equal to a square plus one have this sequence as indices. For example, 25th triangular number is 25*26/2 = 325 = 18^2 + 1. [From Tanya Khovanova & Alexey Radul (tanyakh(AT)yahoo.com), Aug 08 2009]

a(n)={3*A001541(n)-1}/2.

a(n)=3*A001108(n)+1. - David Scheers, Dec 25 2006

a(n)=-1/2+(3/4)*((3+sqrt(8))^n+(3-sqrt(8))^n) for n>=0. a(n)=floor((3/4)*(3+sqrt(8))^n) for n>0. - Franz Vrabec (franz.vrabec(AT)aon.at), Aug 21 2006

G.f.: (1-3x+4x^2)/((1-x)(1-6x+x^2)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 09 2008]

a[n_] := a[n] = 6a[n - 1] - a[n - 2] + 2; a[0] = 1; a[1] = 4; Table[ a[n], {n, 0, 20}]

Cf. A000217, A001108, A001541.

Sequence in context: A156701 A015533 A079291 this_sequence A055846 A091634 A010909

Adjacent sequences: A072218 A072219 A072220 this_sequence A072222 A072223 A072224

nonn

Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 04 2002

Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 08 2002