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Search: id:A030116
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| A030116 |
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Number of distributive lattices; also number of paths with n turns when light is reflected from 12 glass plates. |
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+0
10
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| 1, 12, 78, 650, 5083, 40690, 323401, 2576795, 20514715, 163369570, 1300879372, 10358963615, 82488063476, 656851828075, 5230500095281, 41650400765615, 331661528811227, 2641015991983270, 21030372117368865, 167464549591889570
(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(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 (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=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)
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CROSSREFS
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See also A006356-A006359, A025030, A030112-A030115.
Sequence in context: A121665 A124863 A022577 this_sequence A035042 A061593 A038734
Adjacent sequences: A030113 A030114 A030115 this_sequence A030117 A030118 A030119
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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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