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

Author

Clark Kimberling, Mar 29 2014

Keywords

• nonn
• easy

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.

Examples

			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]
		

Links

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

Crossrefs

Cf. A239881, A239883, A239872.

Programs

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 *)

Extensions

More terms from Alois P. Heinz, Mar 31 2014