0,2

Let M denotes the 4 X 4 matrix = row by row (1,1,1,1)(1,1,1,0)(1,1,0,0)(1,0,0,0) and A(n) the vector (x(n),y(n),z(n),t(n))=M^n*A where A is the vector (1,1,1,1) then a(n)=x(n) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 02 2002

In general, the g.f. for p glass plates is: A(x) = F_{p-1}(-x)/F_p(x) where F_p(x) = Sum_{k=0,p} (-1)^[(k+1)/2]*C([(p+k)/2],k)*x^k. - Paul D. Hanna (pauldhanna(AT)juno.com), Feb 06 2006

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.

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

a(n) is asymptotic to z(4)*w(4)^n where w(4)=(1/2)/cos(4*Pi/9) and z(4) is the root 1<x<2 of P(4, X) = 1+27*X-324*X^2+243*X^3 - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 16 2002

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

Binomial transform of A122167(unsigned): (1, 3, 3, 11, 10, 40, 33, 146,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 24 2007

A006357:=-(-1+z**2-2*z+z**3)/(1+z)/(z**3-3*z+1); [Conjectured by S. Plouffe in his 1992 dissertation.]

(PARI) {a(n)=local(p=4); 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)} (Hanna)

Cf. A000217, A000330, A050446, A050447.

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

Cf. A038197 (4-wave sequence).

Cf. A122167.

Sequence in context: A007713 A058488 A036674 this_sequence A047088 A114946 A001551

Adjacent sequences: A006354 A006355 A006356 this_sequence A006358 A006359 A006360

nonn,nice,easy

njas

Recurrence, alternative description from Jacques Haubrich (jhaubrich(AT)freeler.nl).

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

More terms from Paul D. Hanna (pauldhanna(AT)juno.com), Feb 06 2006