OFFSET
0,9
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..500
FORMULA
EXAMPLE
a(8) counts these 4 partitions: 431, 41111, 3221, 221111.
From Gus Wiseman, Oct 24 2023: (Start)
The a(0) = 1 through a(12) = 12 partitions:
() . . . (211) . . . (431) . . . (633)
(3221) (651)
(41111) (4332)
(221111) (5421)
(33222)
(52221)
(63111)
(432111)
(3222111)
(6111111)
(42111111)
(222111111)
(End)
MATHEMATICA
z = 40; p[n_] := p[n] = IntegerPartitions[n]; f[t_] := f[t] = Length[t]
t1 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] < n &]], {n, z}] (* A239259 *)
t2 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] <= n &]], {n, z}] (* A239260 *)
t3 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] == n &]], {n, z}] (* A239261 *)
t4 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] > n &]], {n, z}] (* A239262 *)
t5 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] >= n &]], {n, z}] (* A239263 *)
(* Peter J. C. Moses, Mar 12 2014 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Mar 13 2014
EXTENSIONS
More terms from Alois P. Heinz, Mar 15 2014
STATUS
approved