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

0,2

Comments

a(n) = number of strict partitions (that is, every part has multiplicity 1) of 2n + 1 having an ordering of the parts in which no two neighboring parts have the same parity. This sequence is nondecreasing, unlike A239881, of which it is a bisection; the other bisection is A239882.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..500

Example

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].

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 *)

Crossrefs

Cf. A239881, A239882, A239872.

Sequence in context: A363067 A038499 A118199 * A332283 A088318 A038083

Adjacent sequences: A239880 A239881 A239882 * A239884 A239885 A239886

Keyword

nonn,easy

Author

Clark Kimberling, Mar 29 2014

Extensions

More terms from Alois P. Heinz, Mar 31 2014

Status

approved