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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 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-François 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 AUTHOR Vladeta Jovovic, Apr 20 2000 STATUS approved

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Last modified January 22 10:25 EST 2020. Contains 331144 sequences. (Running on oeis4.)