0,2

Let M(8) be the 8 X 8 matrix (0,0,0,1)/(0,0,1,1)/(0,0,1,1)/(1,1,1,1) and let v(8) be the vector (1,1,1,1,1,1,1,1); then v(8)*M(8)^n = (x,y,z,t,u,v, w,a(n)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 29 2002

For a k-glass sequence, say a(n,k), a(n,k) is always asymptotic to z(k)*w(k)^n where w(k)=(1/2)/cos(k*Pi/(2k+1)) and it is conjectured that z(k) is the root 1<x<2 of a polynomial of degree Phi(2k+1)/2 - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 16 2002

J. Berman and P. Koehler, Cardinalities of finite distributive lattices, Mitteilungen aus dem Mathematischen Seminar Giessen, 121 (1976), 103-124.

J. Haubrich, Multinacci Rijen [Multinacci sequences], Euclides (Netherlands), Vol. 74, Issue 4, 1998, pp. 131-133.

G. Kreweras, Les preordres totaux compatibles avec un ordre partiel. Math. Sci. Humaines No. 53 (1976), 5-30.

a(n) = 4*a(n-1)+ 10*a(n-2)-10*a(n-3)-15*a(n-4)+ 6*a(n-5)+7*a(n-6)-a(n-7)-a(n-8). - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 09 2002

a(n) is asymptotic to z(8)*w(8)^n where w(8)=(1/2)/cos(8*Pi/17) and z(8) is the root 1<x<2 of P(8, X) = 1+ 204X -12138X^2-324258X^3+4593655X^4+36916282X^5-168962983X^6-410338673X^7+ 410338673X^8 - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 16 2002

(PARI) k=8; M(k)=matrix(k, k, i, j, if(1-sign(i+j-k), 0, 1)); v(k)=vector(k, i, 1); a(n)=vecmax(v(k)*M(k)^n)

See also A006356-A006359, A025030, A030113-A030116.

Sequence in context: A054627 A019022 A079819 this_sequence A001555 A032770 A032794

Adjacent sequences: A030109 A030110 A030111 this_sequence A030113 A030114 A030115

nonn

Jacques Haubrich (jhaubrich(AT)freeler.nl)

More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 29 2002