1,2

The ratio k(n) /(2*j(n)) tends to sqrt(2) as n increases.

The squares of the numbers in this sequence are one less than a triangular number: a(n)^2 = A164080(n). For example, 18^2 is 324, and 325 is a triangular number. a(n)^2 + 1 = A164055(n). a(n)^2 = A072221(n)(A072221(n)+1)/2 - 1. [From Tanya Khovanova & Alexey Radul (tanyakh(AT)yahoo.com), Aug 09 2009]

Index entries for sequences related to linear recurrences with constant coefficients

Tanya Khovanova, Recursive Sequences

j(1)=0, j(2)=3 then j(n)=6*j(n-1)-j(n-2)

j(n) = ((3+2*sqrt(2))^(n-1) - (3-2*sqrt(2))^(n-1))*3/4/sqrt(2). - Max Alekseyev (maxale(AT)gmail.com), Jan 11 2007

G.f.: 3x^2/(1-6x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 17 2008]

a(n)=3*A001109(n) [M. Hasler, Mar 2009] [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 03 2009]

s=0; lst={}; Do[s+=n; If[Sqrt[s-1]==Floor[Sqrt[s-1]], AppendTo[lst, Sqrt[s-1]]], {n, 8!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Apr 02 2009]

Cf. A103328.

Equals (3/4) A005319(n-1).

A164080 Squares that are one less than a triangular number. A164055 Triangular numbers that are one plus a square. A072221 Triangular numbers that are equal to a square plus one have this sequence as indices. [From Tanya Khovanova & Alexey Radul (tanyakh(AT)yahoo.com), Aug 09 2009]

Sequence in context: A009021 A124408 A136779 this_sequence A007277 A025595 A151331

Adjacent sequences: A106325 A106326 A106327 this_sequence A106329 A106330 A106331

nonn

Pierre CAMI (pierrecami(AT)tele2.fr), Apr 29 2005

More terms from Max Alekseyev (maxale(AT)gmail.com), Jan 11 2007