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%I #10 Dec 27 2012 07:02:37
%S 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,
%T 22,21,22,27,29,27,29,36,36,36,36,45,47,45,47,57,58,57,58,69,73,69,73,
%U 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
%N Number of non-squashing partitions of n into odd parts.
%C 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) ).
%H Joerg Arndt, <a href="/A187821/b187821.txt">Table of n, a(n) for n = 0..1000</a>
%e The a(33) = a(35) = 27 non-squashing partitions of 33 and 35 into odd parts are
%e [ 1] [ 17 9 5 1 1 ] [ 1] [ 19 9 5 1 1 ]
%e [ 2] [ 17 9 7 ] [ 2] [ 19 9 7 ]
%e [ 3] [ 17 11 3 1 1 ] [ 3] [ 19 11 3 1 1 ]
%e [ 4] [ 17 11 5 ] [ 4] [ 19 11 5 ]
%e [ 5] [ 17 13 3 ] [ 5] [ 19 13 3 ]
%e [ 6] [ 17 15 1 ] [ 6] [ 19 15 1 ]
%e [ 7] [ 19 7 5 1 1 ] [ 7] [ 21 7 5 1 1 ]
%e [ 8] [ 19 7 7 ] [ 8] [ 21 7 7 ]
%e [ 9] [ 19 9 3 1 1 ] [ 9] [ 21 9 3 1 1 ]
%e [10] [ 19 9 5 ] [10] [ 21 9 5 ]
%e [11] [ 19 11 3 ] [11] [ 21 11 3 ]
%e [12] [ 19 13 1 ] [12] [ 21 13 1 ]
%e [13] [ 21 7 3 1 1 ] [13] [ 23 7 3 1 1 ]
%e [14] [ 21 7 5 ] [14] [ 23 7 5 ]
%e [15] [ 21 9 3 ] [15] [ 23 9 3 ]
%e [16] [ 21 11 1 ] [16] [ 23 11 1 ]
%e [17] [ 23 5 3 1 1 ] [17] [ 25 5 3 1 1 ]
%e [18] [ 23 5 5 ] [18] [ 25 5 5 ]
%e [19] [ 23 7 3 ] [19] [ 25 7 3 ]
%e [20] [ 23 9 1 ] [20] [ 25 9 1 ]
%e [21] [ 25 5 3 ] [21] [ 27 5 3 ]
%e [22] [ 25 7 1 ] [22] [ 27 7 1 ]
%e [23] [ 27 3 3 ] [23] [ 29 3 3 ]
%e [24] [ 27 5 1 ] [24] [ 29 5 1 ]
%e [25] [ 29 3 1 ] [25] [ 31 3 1 ]
%e [26] [ 31 1 1 ] [26] [ 33 1 1 ]
%e [27] [ 33 ] [27] [ 35 ]
%Y Cf. A018819 and A000123 (non-squashing partitions, also binary partitions).
%Y Cf. A088567 (non-squashing partitions into distinct parts)
%K nonn
%O 0,6
%A _Joerg Arndt_, Dec 27 2012
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