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A054724
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Triangle of numbers of inequivalent Boolean functions of n variables with exactly k nonzero values (atoms) under action of complementing group.
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1
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1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 7, 7, 14, 7, 7, 1, 1, 1, 1, 15, 35, 140, 273, 553, 715, 870, 715, 553, 273, 140, 35, 15, 1, 1, 1, 1, 31, 155, 1240, 6293, 28861, 105183, 330460, 876525, 2020239, 4032015, 7063784, 10855425, 14743445, 17678835, 18796230
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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REFERENCES
| M. A. Harrison, Introduction to Switching and Automata Theory. McGraw Hill, NY, 1965, p. 143.
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LINKS
| Index entries for sequences related to Boolean functions
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FORMULA
| 2^(-n)*C(2^n, k) if k is odd and 2^(-n)*(C(2^n, k)+(2^n-1)*C(2^(n-1), k/2)) if k is even.
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EXAMPLE
| [1, 1, 1], [1, 1, 3, 1, 1], [1, 1, 7, 7, 14, 7, 7, 1, 1], ...
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MATHEMATICA
| rows = 5; t[n_, k_?OddQ] := 2^-n*Binomial[2^n, k]; t[n_, k_?EvenQ] := 2^-n*(Binomial[2^n, k] + (2^n-1)*Binomial[2^(n-1), k/2]); Flatten[ Table[ t[n, k], {n, 1, rows}, {k, 0, 2^n}]] (* From Jean-François Alcover, Nov 21 2011, after Vladeta Jovovic *)
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CROSSREFS
| Row sums give A000231. Cf. A052265.
Sequence in context: A124371 A147989 A119329 * A061494 A141901 A200473
Adjacent sequences: A054721 A054722 A054723 * A054725 A054726 A054727
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KEYWORD
| easy,nonn,nice,tabf
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 20 2000
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