0,6

From the conjecture of Zagier, Drinfeld, Kontsevich and Goncharov (see link).

P(0)=P(1)=P(2)=P(3)=1, for m>3: P(m) = P(m-3) + P(m-4) is the 3rd sequence in the series: Fibonacci sequence, Padovan sequence, ... The Padovan sequence (whose ratio of successive terms approaches the plastic constant) is similar to the Perrin sequence. - Jonathan Vos Post (jvospost2(AT)yahoo.com), Jan 23 2005

Binomial transform yields A079398 without the initial (0,1,1,1). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 09 2008

Michel Waldschmidt, "Multiple Zeta values and Euler-Zagier numbers", in Number theory and discrete mathematics, International conference in honour of Srinivasa Ramanujan, Center for Advanced Study in Mathematics, Panjab University, Chandigarh, (Oct 02, 2000).

Michel Waldschmidt, Multiple Zeta values and Euler-Zagier numbers

Eric Weisstein's World of Mathematics, Padovan Sequence.

a(1)=0, a(2)=a(3)=a(4)=1; for n>=4, a(n)=a(n-2)+a(n-3).

a(n)=sum{k=0..floor((n-1)/2), binomial(floor((n-k-1)/3), k)} (offset 0); a(n)=sum{k=0..floor(n/2), binomial(floor((n-k-1)/3), k)}-0^n. (offset 0). - Paul Barry (pbarry(AT)wit.ie), Jul 06 2004

For n>1, a(n) = P(n-2) where P(n) is defined by: P(0)=P(1)=P(2)=P(3)=1, for m>3: P(m) = P(m-3) + P(m-4). - Jonathan Vos Post (jvospost2(AT)yahoo.com), Jan 23 2005

The same sequence may be constructed as follows: Let M = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 1, 0, 0}}; v[1] = {1, 1, 1, 1}; v[n] = M.v[n - 1]. Then a(n) = v[n][[1]]. - Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 16 2006

O.g.f.: -x^2*(1+x+x^2)/(-1+x^3+x^4). a(n)=A017817(n-1)+A017817(n-2)+A017817(n-3). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 09 2008

Cf. A000931.

Adjacent sequences: A079395 A079396 A079397 this_sequence A079399 A079400 A079401

Sequence in context: A077564 A088044 A029051 this_sequence A071988 A029050 A066920

nonn

Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 16 2003