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A030116 Number of distributive lattices; also number of paths with n turns when light is reflected from 12 glass plates. 10
1, 12, 78, 650, 5083, 40690, 323401, 2576795, 20514715, 163369570, 1300879372, 10358963615, 82488063476, 656851828075, 5230500095281, 41650400765615, 331661528811227, 2641015991983270, 21030372117368865, 167464549591889570, 1333517788817519126 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Let M(12) be the 12 X 12 matrix (0,0,0,1)/(0,0,1,1)/(0,1,1,1)/(1,1,1,1) and let v(12) be the 12-vector (1,1,..,1,1,1); then v(12)*M(12)^n = (x(1),x(2),...x(11),a(n)) - Benoit Cloitre, Sep 29 2002

REFERENCES

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.

LINKS

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

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

FORMULA

G.f.: 1/(-x-1/(-x-1/(-x-1/(-x-1/(-x-1/(-x-1/(-x-1/(-x-1/(-x-1/(-x- 1/(-x-1/(-x-1)))))))))))). [From Paul Barry, Mar 24 2010]

PROG

(PARI) k=12; 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)

CROSSREFS

See also A006356-A006359, A025030, A030112-A030115.

Sequence in context: A199492 A200055 A230520 * A200036 A224775 A258480

Adjacent sequences:  A030113 A030114 A030115 * A030117 A030118 A030119

KEYWORD

nonn

AUTHOR

Jacques Haubrich (jhaubrich(AT)freeler.nl)

EXTENSIONS

More terms from Benoit Cloitre, Sep 29 2002

STATUS

approved

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Last modified November 22 13:47 EST 2019. Contains 329393 sequences. (Running on oeis4.)