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A054724 Triangle of numbers of inequivalent Boolean functions of n variables with exactly k nonzero values (atoms) under action of complementing group. 3
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; text; internal format)
OFFSET

1,6

REFERENCES

M. A. Harrison, Introduction to Switching and Automata Theory. McGraw Hill, NY, 1965, p. 143.

LINKS

G. C. Greubel, Table of n, a(n) for the first 10 rows, flattened

Index entries for sequences related to Boolean functions

FORMULA

T(n,k) = 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.

EXAMPLE

[1, 1, 1], [1, 1, 3, 1, 1], [1, 1, 7, 7, 14, 7, 7, 1, 1], ...

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}]] (* Jean-Fran├žois Alcover, Nov 21 2011, after Vladeta Jovovic *)

T[n_, k_]:= If[OddQ[k], Binomial[2^n, k]/2^n, 2^(-n)*(Binomial[2^n, k] + (2^n - 1)*Binomial[2^(n - 1), k/2])]; Table[T[n, k], {n, 1, 5}, {k, 0, 2^n}] //Flatten  (* G. C. Greubel, Feb 15 2018 *)

CROSSREFS

Row sums give A000231. Cf. A052265.

Sequence in context: A124371 A147989 A119329 * A061494 A141901 A200473

Adjacent sequences:  A054721 A054722 A054723 * A054725 A054726 A054727

KEYWORD

easy,nonn,nice,tabf,changed

AUTHOR

Vladeta Jovovic, Apr 20 2000

STATUS

approved

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Last modified February 22 11:16 EST 2018. Contains 299452 sequences. (Running on oeis4.)