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

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 401

Eric Weisstein's World of Mathematics, Tribonacci Number

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

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)lhsystems.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

Cf. A000045, A000073, A027907.

Cf. A027053, A078042.

Adjacent sequences: A001587 A001588 A001589 this_sequence A001591 A001592 A001593

Sequence in context: A010033 A065615 A054182 this_sequence A078042 A115792 A054177

nonn,easy

njas

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

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