A059090 - OEIS

%I #12 Oct 24 2014 15:09:58

%S 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,

%T 1,63,1050,9030,41545,118629,233821,329205,327915,224280,100716,29337,

%U 5950,910,105,7

%N 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).

%C 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.

%D Jovovic V., Kilibarda G., The number of n-variable Boolean functions in the Post class F(7,2), Belgrade, 2001, in preparation.

%D 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.

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

%H <a href="http://search.ieice.or.jp/1997/abs/e80-a_8_1502.htm">Pogosyan et al., The Number of Clique Boolean Functions</a>

%F 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).

%e 1;

%e 1, 1;

%e 1, 3;

%e 1, 7, 3, 1;

%e 1, 15, 30, 30, 5;

%e 1, 31, 195, 605, 780, 543, 300, 135, 45, 10, 1;

%e 1, 63, 1050, 9030, 41545, 118629, 233821, 329205, 327915, 224280, 100716, 29337, 5950, 910, 105, 7;

%Y Cf. A001206, A032263, A051303-A051307, A036239, A051180-A051185, A016269, A047707, A051112-A051118, A000372.

%K hard,tabf,nonn

%O 0,5

%A _Vladeta Jovovic_, Goran Kilibarda, Dec 28 2000