0,2

Let M denotes the 5 X 5 matrix = row by row (1,1,1,1,1)(1,1,1,1,0)(1,1,1,0,0)(1,1,0,0,0)(1,0,0,0,0) and A(n) the vector (x(n),y(n),z(n),t(n),u(n))=M^n*A where A is the vector (1,1,1,1,1); then a(n)=y(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).

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

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

S. J. Cyvin and I. Gutman, Kekule structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see p. 120).

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.

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

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

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

a(n) is asymptotic to z(5)*w(5)^n where w(5)=(1/2)/cos(5*Pi/11) and z(5) is the root 1<x<2 of P(5, X) = -1+55*X+847*X^2-5324*X^3-14641*X^4+14641*X^5 - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 16 2002

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

A=seq(a.j, j=0..4):grammar1:=[Q4, { seq(Q.i=Union(Epsilon, seq(Prod(a.j, Q.j), j=4-i..4)), i=0..4), seq(a.j=Z, j=0..4) }, unlabeled]: seq(count(grammar1, size=j), j=0..23); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 09 2007

A006358:=-(z-1)*(z**3-3*z-1)/(-1+3*z+3*z**2-4*z**3-z**4+z**5); [Conjectured by S. Plouffe in his 1992 dissertation.]

(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=5); 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)}

Cf. A000217, A000330, A050446, A050447.

See also A006356-A006359, A025030, A030112-A030116.

Cf. A038201 (5-wave sequence).

Sequence in context: A002221 A007714 A123011 this_sequence A054108 A149585 A114947

Adjacent sequences: A006355 A006356 A006357 this_sequence A006359 A006360 A006361

nonn,easy,nice

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

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

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