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

0,4

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

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Example

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].

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 *)

Crossrefs

Cf. A239833, A239835, A239880.

Sequence in context: A114209 A132091 A262090 * A051792 A053602 A272912

Adjacent sequences: A239878 A239879 A239880 * A239882 A239883 A239884

Keyword

nonn,easy

Author

Clark Kimberling, Mar 29 2014

Status

approved