A248929 Triangle read by rows: T(n,k) = PIP(n,k) is the number of maximal families of sets from {1,2,...,n} with the property that if A and B are sets in the family, then |AB|>=k.
1, 2, 1, 4, 3, 1, 12, 7, 4, 1, 81, 25, 11, 5, 1, 2646, 216, 46, 16, 6, 1, 1422564, 12784, 477, 77, 22, 7, 1, 229809982112, 11115851, 45104, 925, 120, 29, 8, 1
Offset: 1
Examples
Triangle PIP(n,k) begins: n\k 1 2 3 4 5 6 7... 1 1 2 2 1 3 4 3 1 4 12 7 4 1 5 81 25 11 5 1 6 2646 216 46 16 6 1 7 1422564 12784 477 77 22 7 1 8 229809982112 11115851 45104 925 120 29 8 9 129315 1633 177 37 10 320026 2686 250 11 4181
References
- Ian Anderson, Combinatorics of Finite Sets, Oxford University Press, 1987, pages 1-9.
Crossrefs
Cf. A001206 (first column).
Formula
PIP(k,k)=1
PIP(k+1,k)=C(k+1,1)=k+1
PIP(k+2,k)=C(k+2,2)+1
PIP(k+3,k)=2*C(k+3,3)+C(k+3,1)
PIP(k+4,k)=12*C(k+4,4)+C(k+4,3)+C(k+4,2)+1
Extensions
Term PIP(6,2) (12778 should be 12784) in the data sequence and in the example table corrected by John M. Ingram, Nov 02 2014
Another row added to the data sequence by John M. Ingram, Nov 02 2014
Several new terms added to the example table by John M. Ingram, Nov 02 2014
Comments