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A239262
Number of partitions of n having (sum of odd parts) > (sum of even parts).
5
0, 1, 1, 2, 2, 5, 6, 8, 10, 19, 24, 30, 37, 61, 75, 93, 114, 177, 217, 260, 315, 461, 556, 663, 791, 1137, 1353, 1603, 1892, 2625, 3093, 3622, 4252, 5796, 6790, 7907, 9198, 12299, 14283, 16558, 19142, 25269, 29175, 33607, 38672, 50227, 57723, 66199, 75789
OFFSET
0,4
LINKS
FORMULA
a(n) + A239260(n) = A000041(n).
EXAMPLE
a(8) counts these 10 partitions: 71, 53, 521, 5111, 332, 3311, 32111, 311111, 2111111, 11111111.
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