0,2

Let M(7) be the 7 X 7 matrix: (0,0,0,0,0,0,1)/(0,0,0,0,0,1,1)/(0,0,0,0,1,1,1)/(0,0,0,1,1,1,1)/(0,0,1,1,1,1,1)/(0,1,1,1,1,1,1)/(1,1,1,1,1,1,1) and let v(7) be the vector (1,1,1,1,1,1,1); then v(7)*M(7)^n = (x,y,z,t,u,v,a(n)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 29 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)+6*a(n-2)-10*a(n-3)-5*a(n-4)+6*a(n-5)+a(n-6)-a(n-7).

a(n) is asymptotic to z(7)*w(7)^n where w(7)=(1/2)/cos(7*Pi/15) and z(7) is the root 1<x<2 of P(7, X)=1-120*X-8100*X^2-57375*X^3+50625*X^4 - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 16 2002

A=seq(a.j, j=0..6):grammar1:=[Q6, { seq(Q.i=Union(Epsilon, seq(Prod(a.j, Q.j), j=6-i..6)), i=0..6), seq(a.j=Z, j=0..6) }, unlabeled]: seq(count(grammar1, size=j), j=0..21); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 09 2007

(PARI) k=7; 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, A030112-A030116.

Sequence in context: A037597 A037702 A054626 this_sequence A001554 A026664 A058822

Adjacent sequences: A025027 A025028 A025029 this_sequence A025031 A025032 A025033

nonn

Jacques Haubrich (jhaubrich(AT)freeler.nl)

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