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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.
8
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.
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
Column k=-1 of A240009.
Sequence in context: A163227 A325690 A238779 * A240010 A283502 A324756
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Mar 29 2014
STATUS
approved