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

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