0,4

Number of (n-1)-bit binary sequences with each one adjacent to a zero. - Ron Hardin (rhh(AT)cadence.com), Dec 24 2007

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.

B. G. Baumgart, Letter to the editor, Fib. Quart. 2 (1964), 260, 302.

M. Feinberg, Fibonacci-Tribonacci, Fib. Quart. 1(#3) (1963), 71-74.

T. D. Noe, Table of n, a(n) for n = 0..200

Joerg Arndt, Fxtbook

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, Tribonacci Number

Nick Hobson, Python program for this sequence

G.f.: (1-x)*(1+x)/(1-x-x^2-x^3). - Ralf Stephan, Feb 11 2004

a(n) = rightmost term of M^n * [1 1 1], where M = the 3X3 matrix [1 1 1 / 1 0 0 / 0 1 0]. (M^n * [1 1 1]= [a(n+2) a(n+1) a(n)]). a(n)/a(n-1) tends to the tribonacci constant, 1.839286755...; an eigenvalue of M and a root of x^3 - x^2 - x - 1 = 0. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 17 2004

a(n)=A001590(n+3)-A001590(n+2); a(n+1)-a(n)=2*A000073(n); a(n)=A000073(n+3)-A000073(n+1). - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), May 22 2006

a(n)=A001590(n)+A001590(n+1) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 25 2006

K:=(1-z^2)/(1-z-z^2-z^3): Kser:=series(K, z=0, 45): seq((coeff(Kser, z, n)), n= 0..34); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 08 2007

A000213:=(z-1)*(1+z)/(-1+z+z**2+z**3); [Conjectured by S. Plouffe in his 1992 dissertation.]

Cf. A000288, A000322, A000383, A046735, A060455.

Adjacent sequences: A000210 A000211 A000212 this_sequence A000214 A000215 A000216

Sequence in context: A102475 A066173 A114322 this_sequence A074858 A074860 A135728

easy,nonn,nice

njas