A239881 Number of strict partitions of n having an ordering in which no parts of equal parity are juxtaposed.

1, 1, 1, 2, 1, 3, 2, 5, 3, 7, 6, 10, 9, 13, 15, 18, 22, 23, 33, 31, 46, 41, 65, 55, 87, 73, 117, 99, 153, 132, 199, 177, 254, 236, 324, 313, 408, 412, 512, 540, 639, 701, 795, 904, 986, 1159, 1221, 1473, 1509, 1861, 1862, 2336, 2298, 2915, 2830, 3615, 3485

Offset: 0

Author

Clark Kimberling, Mar 29 2014

Keywords

• nonn
• easy

Comments

A strict partition is one in which every part has multiplicity 1.

a(n) = Sum_{k=-1..1} A240021(n,k). - Alois P. Heinz, Apr 02 2014

Examples

			a(12) counts these 9 partitions:  [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..1000

Crossrefs

Cf. A239833, A239835, A239880.

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[n]], {n, 0, 60}]  (* A239880 *)
(* Peter J. C. Moses, Mar 10 2014 *)