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Search: id:A030113
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| A030113 |
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Number of distributive lattices; also number of paths with n turns when light is reflected from 9 glass plates. |
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+0
2
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| 1, 9, 45, 285, 1695, 10317, 62349, 377739, 2286648, 13846117, 83833256, 507596153, 3073376281, 18608642427, 112671254094, 682200039446, 4130572919575, 25009722123505, 151428434581516, 916866281219258
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Let M(9) be the 9 X 9 matrix (0,0,0,1)/(0,0,1,1)/(0,0,1,1)/(1,1,1,1) and let v(9) be the vector (1,1,1,1,1,1,1,1,1); then v(9)*M(9)^n = (x,y,z,t,u,v, w,m,a(n)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 29 2002
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REFERENCES
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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.
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PROGRAM
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(PARI) k=9; 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)
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CROSSREFS
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See also A006356-A006359, A025030, A030112-A030116.
Sequence in context: A054628 A132133 A009410 this_sequence A001556 A009432 A058824
Adjacent sequences: A030110 A030111 A030112 this_sequence A030114 A030115 A030116
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KEYWORD
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nonn
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AUTHOR
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Jacques Haubrich (jhaubrich(AT)freeler.nl)
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EXTENSIONS
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More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 29 2002
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