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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

%I

%S 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,

%T 553,273,140,35,15,1,1,1,1,31,155,1240,6293,28861,105183,330460,

%U 876525,2020239,4032015,7063784,10855425,14743445,17678835,18796230

%N Triangle of numbers of inequivalent Boolean functions of n variables with exactly k nonzero values (atoms) under action of complementing group.

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

%H G. C. Greubel, <a href="/A054724/b054724.txt">Table of n, a(n) for the first 10 rows, flattened</a>

%H <a href="/index/Bo#Boolean">Index entries for sequences related to Boolean functions</a>

%F 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.

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

%t 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 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 *)

%Y Row sums give A000231. Cf. A052265.

%K easy,nonn,nice,tabf

%O 1,6

%A _Vladeta Jovovic_, Apr 20 2000

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Last modified February 24 22:00 EST 2020. Contains 332216 sequences. (Running on oeis4.)