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Limit of the position distance between the n-th odd partition of even numbers and its successor in the list of all integer partitions sorted in reverse lexicographic order; also first differences of A186131.

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`%I #8 May 17 2015 13:27:04
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`%S 3,2,6,3,3,12,3,4,3,4,23,3,5,3,7,2,4,5,43,3,5,3,8,3,2,4,13,3,5,6,78,3,
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`%T 5,3,9,3,2,4,15,2,7,3,5,19,3,4,6,7,136,3,5,3,9,3,2,4,16,3,2,7,3,5,27,
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`%U 3,3,10,3,4,6,28,2,4,5,7,8,232,3,5,3,9,3,2,4,17,3,2,7,3,5,30,2,6,3,3,10,3,4,6,46,4
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`%N Limit of the position distance between the n-th odd partition of even numbers and its successor in the list of all integer partitions sorted in reverse lexicographic order; also first differences of A186131.
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`%H Alois P. Heinz, <a href="/A186204/b186204.txt">Table of n, a(n) for n = 1..10000</a>
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`%e For a large even number k the first partitions in reverse lexicographic
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`%e order are [k], [k-1,1], [k-2,2], [k-2,1,1], [k-3,3] ..., where only the
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`%e partitions in positions 2, 5, ... consist of odd parts alone, thus
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`%e a(1) = 5-2 = 3.
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`%Y Cf. A186131.
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`%K nonn,look
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`%O 1,1
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`%A _Alois P. Heinz_, Feb 14 2011
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