A272187 Number of strongly decreasing partitions of n into odd parts.

1, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 5, 4, 5, 6, 7, 6, 7, 8, 10, 8, 10, 11, 13, 11, 13, 14, 17, 14, 17, 19, 21, 19, 21, 24, 27, 24, 27, 31, 33, 31, 33, 38, 41, 38, 41, 48, 49, 48, 49, 58, 60, 58, 60, 71, 71, 71, 71, 84, 85, 84, 85, 101, 99, 101, 99, 118, 118, 118, 118, 139, 137, 139

Offset: 0

Author

Joerg Arndt, Apr 22 2016

Keywords

• nonn

Comments

A strongly decreasing partition of n is a partition p(1) + p(2) + ... + p(m) = n such that p(k) > sum(j=k+1..m, p(j) ).

Examples

			The a(30) = 11 such partitions are:
01:   [ 17 7 5 1 ]
02:   [ 17 9 3 1 ]
03:   [ 17 13 ]
04:   [ 19 7 3 1 ]
05:   [ 19 11 ]
06:   [ 21 5 3 1 ]
07:   [ 21 9 ]
08:   [ 23 7 ]
09:   [ 25 5 ]
10:   [ 27 3 ]
11:   [ 29 1 ]
		

Links

• Joerg Arndt, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A187821 (non-squashing partitions of n into odd parts), A040039 (strongly decreasing partitions).