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A187821
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Number of non-squashing partitions of n into odd parts.
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3
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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
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OFFSET
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0,6
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COMMENTS
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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) ).
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LINKS
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EXAMPLE
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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 ]
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CROSSREFS
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Cf. A018819 and A000123 (non-squashing partitions, also binary partitions).
Cf. A088567 (non-squashing partitions into distinct parts)
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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