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A030115
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Number of distributive lattices; also number of paths with n turns when light is reflected from 11 glass plates.
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1
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1, 11, 66, 506, 3641, 26818, 196119, 1437799, 10532302, 77173602, 565424068, 4142793511, 30353430420, 222394369223, 1629443428021, 11938642758854, 87472304803355, 640893994357062, 4695716053827835, 34404674660198306
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Let M(11) be the 11 X 11 matrix (0,0,0,1)/(0,0,1,1)/(0,1,1,1)/(1,1,1,1) and let v(11) be the vector (1,1,1,1,1,1,1,1,1); then v(11)*M(11)^n = (x,y,z,t,u,v, w,m,n,o,a(n)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 29 2002
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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.
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PROG
| (PARI) k=11; 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
| See also A006356-A006359, A025030, A030112-A030116.
Sequence in context: A001287 A022576 A000460 * A091929 A058883 A141969
Adjacent sequences: A030112 A030113 A030114 * A030116 A030117 A030118
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KEYWORD
| nonn
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AUTHOR
| Jacques Haubrich (jhaubrich(AT)freeler.nl)
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EXTENSIONS
| More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 29 2002
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