A239882 Number of strict partitions of 2n having an ordering of the parts in which no two neighboring parts have the same parity.

1, 1, 1, 2, 3, 6, 9, 15, 22, 33, 46, 65, 87, 117, 153, 199, 254, 324, 408, 512, 639, 795, 986, 1221, 1509, 1862, 2298, 2830, 3485, 4285, 5267, 6460, 7920, 9687, 11836, 14426, 17557, 21310, 25823, 31204, 37632, 45262, 54326, 65029, 77678, 92549, 110035, 130509

Offset

0,4

Comments

a(n) = number of strict partitions (that is, every part has multiplicity 1) of 2n 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 A239883.

Links

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

Example

a(6) counts these 9 partitions of 12:  [12], [9,2,1], [3,8,1], [7,4,1], [7,2,3], [5,6,1], [6,3,2,1], [5,4,3], [5,4,1,2]

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]], {n, 0, 40}]  (* A239882 *)
(* Peter J. C. Moses, Mar 10 2014 *)

Crossrefs

Cf. A239881, A239883, A239872.

Sequence in context: A256975 A364841 A355980 * A086642 A308930 A304620

Adjacent sequences: A239879 A239880 A239881 * A239883 A239884 A239885

Keyword

nonn,easy

Author

Clark Kimberling, Mar 29 2014

Extensions

More terms from Alois P. Heinz, Mar 31 2014

Status

approved