0,2

Let M denotes the 6 X 6 matrix = row by row (1,1,1,1,1,1)(1,1,1,1,1,0)(1,1,1,1,0,0)(1,1,1,0,0,0)(1,1,0,0,0,0)(1,0,0,0,0,0) and A(n) the vector (x(n),y(n),z(n),t(n),u(n),v(n))=M^n*A where A is the vector (1,1,1,1,1,1) then a(n)=x(n) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 02 2002

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

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

Manfred Goebel, Rewriting Techniques and Degree Bounds for Higher Order Symmetric Polynomials, Applicable Algebra in Engineering, Communication and Computing (AAECC), Volume 9, Issue 6 (1999), 559-573.

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.

G.f. from M. Goebel (manfredg(AT)ICSI.Berkeley.EDU) Jul 26 1997: -(z^4 + z^3 - 3z^2 - 2z + 1) / (-1 + 3z + 6z^2 - 4z^3 - 5z^4 + z^5 + z^6).

a(n)=3*a(n-1)+6*a(n-2)-4*a(n-3)-5*a(n-4)+a(n-5)+a(n-6).

a(n) is asymptotic to z(6)*w(6)^n where w(6)=(1/2)/cos(6*Pi/13) and z(6) is the root 1<x<2 of P(6, X) = -1-91*X+2366*X^2+26364*X^3-142805*X^4-371293*X^5+371293*X^6 - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 16 2002

G.f.: A(x) = (1+3*x-3*x^2-4*x^3+x^4+x^5)/(1-3*x-6*x^2+4*x^3+5*x^4-x^5-x^6). - Paul D. Hanna (pauldhanna(AT)juno.com), Feb 06 2006

A=seq(a.j, j=0..5):grammar1:=[Q5, { seq(Q.i=Union(Epsilon, seq(Prod(a.j, Q.j), j=5-i..5)), i=0..5), seq(a.j=Z, j=0..5) }, unlabeled]: seq(count(grammar1, size=j), j=0..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 09 2007

(PARI) k=5; 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)

(PARI) {a(n)=local(p=6); polcoeff(sum(k=0, p-1, (-1)^((k+1)\2)*binomial((p+k-1)\2, k)* (-x)^k)/sum(k=0, p, (-1)^((k+1)\2)*binomial((p+k)\2, k)*x^k+x*O(x^n)), n)} - Paul D. Hanna (pauldhanna(AT)juno.com), Feb 06 2006

Cf. A000217, A000330, A050446, A050447, A006356, A006357, A006358.

See also A025030, A030112-A030116.

Sequence in context: A137966 A005498 A002222 this_sequence A001553 A009247 A093774

Adjacent sequences: A006356 A006357 A006358 this_sequence A006360 A006361 A006362

nonn,easy

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

Alternative description from Jacques Haubrich (jhaubrich(AT)freeler.nl).

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 24 1999