login
A239259
Number of partitions of n having (sum of odd parts) < (sum of even parts).
5
0, 0, 1, 1, 2, 2, 5, 7, 8, 11, 18, 26, 28, 40, 60, 83, 87, 120, 168, 230, 242, 331, 446, 592, 619, 821, 1083, 1407, 1496, 1940, 2511, 3220, 3393, 4347, 5520, 6976, 7399, 9338, 11732, 14627, 15508, 19314, 23999, 29654, 31519, 38907, 47835, 58555, 62090, 75942
OFFSET
0,5
LINKS
FORMULA
a(n) + A239263(n) = A000041(n).
EXAMPLE
a(8) counts these 8 partitions: 8, 62, 611, 44, 422, 4211, 2222, 22211.
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
STATUS
approved