A239832 Number of partitions of n having 1 more even part than odd, so that there is an ordering of parts for which the even and odd parts alternate and the first and last terms are even.

0, 0, 1, 0, 1, 1, 1, 2, 2, 4, 3, 7, 6, 11, 11, 17, 19, 27, 31, 41, 51, 62, 79, 95, 121, 142, 182, 212, 269, 314, 393, 459, 570, 665, 816, 958, 1160, 1364, 1639, 1928, 2297, 2706, 3200, 3768, 4434, 5212, 6105, 7170, 8361, 9799, 11396, 13322, 15450, 18022

Offset

0,8

Comments

Let c(n) be the number of partitions of n having 1 more odd part than even, so that there is an ordering of parts for which the even and odd parts alternate and the first and last terms are odd. Then c(n) = a(n+1) for n >= 0.

Links

Table of n, a(n) for n=0..53.

Example

The three partitions counted by a(10) are [10], [4,1,2,1,2], and [2,3,2,1,2].

Mathematica

p[n_] := p[n] = Select[IntegerPartitions[n], Count[#, _?OddQ] == -1 + Count[#, _?EvenQ] &]; t = Table[p[n], {n, 0, 10}]
TableForm[t] (* shows the partitions *)
Table[Length[p[n]], {n, 0, 30}]  (* A239832 *)
(* Peter J. C. Moses, Mar 10 2014 *)

Crossrefs

Cf. A239833, A239835, A045931, A239871.

Column k=-1 of A240009.

Sequence in context: A163227 A325690 A238779 * A240010 A283502 A324756

Adjacent sequences: A239829 A239830 A239831 * A239833 A239834 A239835

Keyword

nonn,easy

Author

Clark Kimberling, Mar 29 2014

Status

approved