0,1

Same as Pisot sequence L(2,3)

Length of the continued fraction for sum(k=0,n,1/3^(2^k)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 12 2003

See also A004119 for a(n) = 2a(n-1)-1 with first term =1 . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Feb 20 2004

From the second term on (n>=1), in base 2, these numbers present the pattern 1000...0001 (with n-1 zeros), which is the "opposite" of the binary 2^n-2: (0)111...1110 (cf. A000918). - Alexandre Wajnberg (alexandre.wajnberg(AT)ulb.ac.be), May 31 2005

Numbers n for which the expression 2^n/(n-1) is an integer. - Paolo P. Lava (ppl(AT)spl.at), May 12 2006

a(n) = A127904(n+1) for n>0. - Reinhard Zumkeller, Feb 05 2007

P. Bachmann, Niedere Zahlentheorie (1902, 1910), reprinted Chelsea, NY, 1968, vol. 2, p. 75.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 114

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 362

Zerinvary Lajos, Sage Notebooks

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

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

Eric Weisstein's World of Mathematics, Rudin-Shapiro Sequence

a(n) = 2a(n-1) - 1 = 3a(n-1) - 2a(n-2).

G.f.: (2-3*x)/((1-x)*(1-2*x)).

First differences of A052944 - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 04 2004

a(0) = 1, then a(n) = (Sum i=0..n-1 a(i)) - (n-2). - Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), Jul 10 2004

Inverse binomial transform of A007689. Also, V sequence in Lucas sequence L(3, 2). - Ross La Haye (rlahaye(AT)new.rr.com), Feb 07 2005

Equals binomial transform of [2, 1, 1, 1,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 23 2008

a(n)=A000079(n)+1. - Omar E. Pol (info(AT)polprimos.com), May 18 2008

A000051:=-(-2+3*z)/(2*z-1)/(z-1); [S. Plouffe in his 1992 dissertation.]

Table[2^n + 1, {n, 0, 33}]

(PARI) a(n)=if(n<0, 0, 2^n+1)

sage: [lucas_number2(n, 3, 2) for n in range(37)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 25 2008

Apart from the intial 1, identical to A094373..

See A008776 for definitions of Pisot sequences. Cf. A034472, A052539, A034474, A062394, A034491, A062395, A062396, A007689, A063376, A063481, A074600 - A074624.

Cf. A052944.

Column 2 of array A103438.

Cf. A000079.

Sequence in context: A005257 A091697 A109740 this_sequence A094373 A061902 A110113

Adjacent sequences: A000048 A000049 A000050 this_sequence A000052 A000053 A000054

easy,nonn

njas