A238954 Maximal size of an antichain in graded colexicographic order of exponents.

1, 1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 6, 1, 2, 3, 4, 5, 7, 10, 1, 2, 3, 4, 4, 6, 7, 8, 10, 14, 20, 1, 2, 3, 4, 4, 6, 7, 8, 8, 11, 13, 15, 18, 25, 35, 1, 2, 3, 4, 5, 4, 6, 8, 9, 10, 8, 12, 14, 16, 19, 16, 22, 26, 30, 36, 50, 70, 1, 2, 3, 4, 5, 4, 6, 8, 9, 9, 11, 12, 8, 12, 15, 17, 19, 22, 16, 23, 26, 30, 35, 31, 41, 48, 56, 66, 91, 126

Offset: 0

Author

Sung-Hyuk Cha, Mar 07 2014

Keywords

• nonn
• tabf

Examples

			Triangle T(n,k) begins:
  1;
  1;
  1, 2;
  1, 2, 3;
  1, 2, 3, 4, 6;
  1, 2, 3, 4, 5, 7, 10;
  1, 2, 3, 4, 4, 6,  7, 8, 10, 14, 20;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..2713 (rows 0..20)
• S.-H. Cha, E. G. DuCasse, and L. V. Quintas, Graph Invariants Based on the Divides Relation and Ordered by Prime Signatures, arxiv:1405.5283 [math.NT], 2014.

Crossrefs

Cf. A096825 in graded colexicographic order.

Cf. A036035, A238967.

Programs

PARI

\\ here b(n) is A096825.
b(n)={my(h=bigomega(n)\2); sumdiv(n, d, bigomega(d)==h)}
N(sig)={prod(k=1, #sig, prime(k)^sig[k])}
Row(n)={apply(s->b(N(s)), [Vecrev(p) | p<-partitions(n)])}
{ for(n=0, 6, print(Row(n))) } \\ Andrew Howroyd, Apr 25 2020

Formula

T(n,k) = A096825(A036035(n,k)).

Extensions

Offset changed and terms a(50) and beyond from Andrew Howroyd, Apr 25 2020