0,4

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

The binomial transform is A099216. The inverse binomial transform is (-1)^n*A124395(n). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 19 2008]

Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 27 2009: (Start)

Equals INVERT transform of (1, 0, 2, 0, 2, 0, 2,...). a(6) = 17 =

(1, 1, 1, 3, 5, 9) dot (0, 2, 0, 2, 0, 1) = (0 + 2 + 0 + 6 + 0 + 9) = 17. (End)

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

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

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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

Joerg Arndt, Fxtbook

Nick Hobson, Python program for this sequence

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

Index entries for sequences related to linear recurrences with constant coefficients

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)gmail.com), May 22 2006

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

a(n) ~ (F - 1) * T^n, where F = A086254 and T = A058265. [From Charles R Greathouse IV Nov 09 2008]

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); [S. Plouffe in his 1992 dissertation.]

a=1; b=1; c=1; lst={a, b, c}; Do[d=a+b+c; AppendTo[lst, d]; a=b; b=c; c=d, {n, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 30 2008]

sage: from sage.combinat.sloane_functions import recur_gen3 sage: it = recur_gen3(1, 1, 1, 1, 1, 1) sage: [it.next() for i in range(35)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 25 2008

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

N. J. A. Sloane (njas(AT)research.att.com).