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A059090
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Triangle T(n,m) giving number of m-element intersecting antichains on a labeled n-set or n-variable Boolean functions with m nonzero values in the Post class F(7,2), m=0,.., A037952(n).
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1
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1, 1, 1, 1, 3, 1, 7, 3, 1, 1, 15, 30, 30, 5, 1, 31, 195, 605, 780, 543, 300, 135, 45, 10, 1, 1, 63, 1050, 9030, 41545, 118629, 233821, 329205, 327915, 224280, 100716, 29337, 5950, 910, 105, 7
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| An antichain is called intersecting (or proper) antichain if every two members have a nonempty intersection. Row sums give the number of intersecting antichains on a labeled n-set or n-variable Boolean functions in the Post class F(7,2) or self-dual monotone Boolean functions of n+1 variables. Cf. A001206.
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REFERENCES
| Jovovic V., Kilibarda G., The number of n-variable Boolean functions in the Post class F(7,2), Belgrade, 2001, in preparation.
Pogosyan G., Miyakawa M., Nozaki A., Rosenberg I., The Number of Clique Boolean Functions, IEICE Trans. Fundamentals, Vol. E80-A, No. 8, pp. 1502-1507, 1997/8.
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LINKS
| Index entries for sequences related to Boolean functions
Pogosyan et al., The Number of Clique Boolean Functions
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FORMULA
| T(n, 0)=1, T(n, 1)=2^n-1, T(n, 2)=A032263(n), T(n, 3)=A051303(n), T(n, 4)=A051304(n), T(n, 5)=A051305(n), T(n, 6)=A051306(n), T(n, 7)=A051307(n).
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EXAMPLE
| [1], [1, 1], [1, 3], [1, 7, 3, 1], [1, 15, 30, 30, 5], [1, 31, 195, 605, 780, 543, 300, 135, 45, 10, 1], [1, 63, 1050, 9030, 41545, 118629, 233821, 329205, 327915, 224280, 100716, 29337, 5950, 910, 105, 7].
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CROSSREFS
| Cf. A001206, A032263, A051303-A051307, A036239, A051180-A051185, A016269, A047707, A051112-A051118, A000372.
Sequence in context: A065289 A065265 A132885 * A133115 A104797 A130330
Adjacent sequences: A059087 A059088 A059089 * A059091 A059092 A059093
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KEYWORD
| hard,nonn
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AUTHOR
| Vladeta Jovovic, Goran Kilibarda (vladeta(AT)eunet.rs), Dec 28 2000
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