A187821 Number of non-squashing partitions of n into odd parts.

1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 4, 3, 4, 5, 6, 5, 6, 7, 9, 7, 9, 11, 12, 11, 12, 15, 17, 15, 17, 21, 22, 21, 22, 27, 29, 27, 29, 36, 36, 36, 36, 45, 47, 45, 47, 57, 58, 57, 58, 69, 73, 69, 73, 86, 88, 86, 88, 103, 109, 103, 109, 125, 130, 125, 130, 147, 157, 147, 157, 176, 184, 176, 184, 205, 220, 205, 220, 241, 256, 241, 256

Offset: 0

Author

Joerg Arndt, Dec 27 2012

Keywords

• nonn

Comments

A non-squashing 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(33) = a(35) = 27 non-squashing partitions of 33 and 35 into odd parts are
[ 1]   [ 17 9 5 1 1 ]       [ 1]   [ 19 9 5 1 1 ]
[ 2]   [ 17 9 7 ]           [ 2]   [ 19 9 7 ]
[ 3]   [ 17 11 3 1 1 ]      [ 3]   [ 19 11 3 1 1 ]
[ 4]   [ 17 11 5 ]          [ 4]   [ 19 11 5 ]
[ 5]   [ 17 13 3 ]          [ 5]   [ 19 13 3 ]
[ 6]   [ 17 15 1 ]          [ 6]   [ 19 15 1 ]
[ 7]   [ 19 7 5 1 1 ]       [ 7]   [ 21 7 5 1 1 ]
[ 8]   [ 19 7 7 ]           [ 8]   [ 21 7 7 ]
[ 9]   [ 19 9 3 1 1 ]       [ 9]   [ 21 9 3 1 1 ]
[10]   [ 19 9 5 ]           [10]   [ 21 9 5 ]
[11]   [ 19 11 3 ]          [11]   [ 21 11 3 ]
[12]   [ 19 13 1 ]          [12]   [ 21 13 1 ]
[13]   [ 21 7 3 1 1 ]       [13]   [ 23 7 3 1 1 ]
[14]   [ 21 7 5 ]           [14]   [ 23 7 5 ]
[15]   [ 21 9 3 ]           [15]   [ 23 9 3 ]
[16]   [ 21 11 1 ]          [16]   [ 23 11 1 ]
[17]   [ 23 5 3 1 1 ]       [17]   [ 25 5 3 1 1 ]
[18]   [ 23 5 5 ]           [18]   [ 25 5 5 ]
[19]   [ 23 7 3 ]           [19]   [ 25 7 3 ]
[20]   [ 23 9 1 ]           [20]   [ 25 9 1 ]
[21]   [ 25 5 3 ]           [21]   [ 27 5 3 ]
[22]   [ 25 7 1 ]           [22]   [ 27 7 1 ]
[23]   [ 27 3 3 ]           [23]   [ 29 3 3 ]
[24]   [ 27 5 1 ]           [24]   [ 29 5 1 ]
[25]   [ 29 3 1 ]           [25]   [ 31 3 1 ]
[26]   [ 31 1 1 ]           [26]   [ 33 1 1 ]
[27]   [ 33 ]               [27]   [ 35 ]
		

Links

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

Crossrefs

Cf. A018819 and A000123 (non-squashing partitions, also binary partitions).

Cf. A088567 (non-squashing partitions into distinct parts)