A157046 Maximum number of partitions of n into exactly k parts, each <= k. a(n) is maximum in each row of A157044.

1, 1, 1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 16, 19, 24, 31, 37, 46, 58, 70, 86, 104, 127, 156, 185, 222, 273, 326, 392, 463, 556, 669, 792, 939, 1109, 1317, 1564, 1838, 2156, 2535, 2986, 3514, 4100, 4777, 5577, 6526, 7621, 8847, 10251, 11869, 13807, 16032, 18529, 21370

Offset: 0

Author

Wouter Meeussen, Feb 22 2009

Keywords

• nonn

Comments

Without the constraint on each part being <= k: see A008284 and A002569.

Examples

			For n=9 the counts of partitions for k=1..9 is 0,0,1,4,5,3,2,1,1 so the maximum is 5 (at k=5).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A157044, A047993, A008284, A002569.

Programs

Maple

b:= proc(n, i, t) option remember; `if`(n=0, 1,
     `if`(i*t max(seq(b(n-i, min(n-i, i-1), i), i=0..n)):
seq(a(n), n=0..55);  # Alois P. Heinz, May 12 2022

Mathematica

Max @@@ Table[T[n,k,k]-T[n,k-1,k],{n,1,128},{k,n}] (* with T[n,a,b] as defined in A047993 *)

Extensions

a(0)=1 prepended by Alois P. Heinz, May 12 2022