1,2

For n>=4, A051009(n) = A098890(n-2) - A098890(n-3) - Kieren MacMillan (kieren(AT)alumni.rice.edu), Dec 19 2007

(2^n)-th Pell numbers [From Sergio Falcon (sfalcon(AT)dma.ulpgc.es), Dec 04 2008]

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Eric Weisstein's World of Mathematics, Pythagoras's Constant

a(n) = 2*a(n-1)*A001601(n-1) - Joe Keane (jgk(AT)jgk.org), May 31 2002

sqrt(2) = 1 + 1/2 - sum_{n=3, infinity} (1/a(n)). - Donald S. McDonald (don.mcdonald(AT)paradise.net.nz), Jan 21 2003

For n>1: a(n)=2a(n-1)*sqrt(2a(n-1)^2+1). - Mario Catalani (mario.catalani(AT)unito.it), May 27 2003

For n>0: a(n)=sum(binomial[2^n, 2r+1]2^r, r=0, .., 2^(n-1)-1) - Mario Catalani (mario.catalani(AT)unito.it), May 30 2003

a(n)=(1/(2 Sqrt[2])) ((1 + Sqrt[2])^(2^n) - (1 - Sqrt[2])^(2^n))]], {n, 0, 7}] [From Artur Jasinski (grafix(AT)csl.pl), Oct 10 2008]

Table[Simplify[Expand[(1/(2 Sqrt[2])) ((1 + Sqrt[2])^(2^n) - (1 - Sqrt[2])^(2^n))]], {n, 0, 7}] [From Artur Jasinski (grafix(AT)csl.pl), Oct 10 2008]

Do[Print[Fibonacci[2^n, 2]], {n, 0, 10}] [From Sergio Falcon (sfalcon(AT)dma.ulpgc.es), Dec 04 2008]

Cf. A001601.

a(n) = A000129(2^n).

Cf. A098890.

A000129 [From Sergio Falcon (sfalcon(AT)dma.ulpgc.es), Dec 04 2008]

Adjacent sequences: A051006 A051007 A051008 this_sequence A051010 A051011 A051012

Sequence in context: A009706 A012551 A156509 this_sequence A060942 A072446 A015181

nonn,frac

Eric Weisstein (eric(AT)weisstein.com)