0,5

Dimensions of the homogeneous components of the higher order peak algebra associated to cubic roots of unity (Hilbert series = 1+1*t+2*t^2+3*t^3+6*t^4+11*t^5 ...) - Jean-Yves Thibon (jyt(AT)univ-mlv.fr), Oct 22 2006

Starting with offset 3: (1, 2, 3, 6, 11, 10, 37,...) = row sums of triangle A145579. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 13 2008]

Starting (1, 2, 3, 6, 1l,...) = INVERT transform of the periodic sequence (1, 1, 0, 1, 1, 0, 1, 1, 0,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), May 04 2009]

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

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

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

M. Feinberg, New slants, Fib. Quart., 2 (1964), 223-227.

M. E. Waddill and L. Sacks, Another generalized Fibonacci sequence, Fib. Quart., 5 (1967), 209-222.

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

Index entries for sequences related to linear recurrences with constant coefficients

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 401

D. Krob and J.-Y. Thibon, Higher order peak algebras

Eric Weisstein's World of Mathematics, Tribonacci Number

Limit a(n)/a(n-1)=x where x^3=1+x+x^2, x=1.839286755.... Let T(n)=A000073=0, 0, 1, 1, 2, 4, 7, 13... x^0=1 and for n>0 x^n=T(n-1)+a(n)*x+T(n)*x^2.

a(3n)=Sum(k+l+m=n)(n!/k!l!m!)*a(l+2m). Example: a(12)=a(8)+4a(7)+10a(6)+16a(5)+19a(4)+16a(3)+10a(2)+4a(1)+a(0) The coefficients are the trinomial coefficients. T(n) and T(n-1) also satisfy this equation. (T(-1)=1)

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

a(n)=A000073(n+1)-A000073(n); a(n)=A000073(n-1)+A000073(n-2) for n>1; A000213(n-2)=a(n+1)-a(n) for n>1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 22 2006

a(n)+a(n+1)=A000213(n) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 25 2006

a(12)=a(11)+a(10)+a(9): 230=125+68+37

a=0; b=1; c=0; 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]

Cf. A000045, A000073, A027907, A001590.

Cf. A027053, A078042.

A145579 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 13 2008]

Adjacent sequences: A001587 A001588 A001589 this_sequence A001591 A001592 A001593

Sequence in context: A010033 A065615 A054182 this_sequence A078042 A115792 A054177

nonn,easy

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

More terms from Henry Bottomley (se16(AT)btinternet.com), Jun 26 2001

Additional comments from Miklos Kristof (kristmikl(AT)freemail.hu), Jul 03 2002