A239883 Number of strict partitions of 2n + 1 having an ordering of the parts in which no two neighboring parts have the same parity.
1, 2, 3, 5, 7, 10, 13, 18, 23, 31, 41, 55, 73, 99, 132, 177, 236, 313, 412, 540, 701, 904, 1159, 1473, 1861, 2336, 2915, 3615, 4463, 5478, 6698, 8152, 9887, 11944, 14391, 17280, 20703, 24739, 29506, 35115, 41730, 49501, 58650, 69389, 82009, 96807, 114175
Offset: 0
Examples
a(5) counts these 10 partitions of 11: [11], [10,1], [9,2], [8,3], [8,1,2], [7,4], [6,5], [6,1,4], [6,3,2], [4,5,2].
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..500
Programs
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Mathematica
d[n_] := Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &]; p[n_] := p[n] = Select[d[n], Abs[Count[#, ?OddQ] - Count[#, ?EvenQ]] <= 1 &]; t = Table[p[n], {n, 0, 12}] TableForm[t] (* shows the partitions *) u = Table[Length[p[2 n + 1]], {n, 0, 20}] (* A239883 *) (* Peter J. C. Moses, Mar 10 2014 *)
Extensions
More terms from Alois P. Heinz, Mar 31 2014
Comments