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%I #7 Mar 15 2014 17:00:08
%S 0,0,1,1,2,2,5,7,8,11,18,26,28,40,60,83,87,120,168,230,242,331,446,
%T 592,619,821,1083,1407,1496,1940,2511,3220,3393,4347,5520,6976,7399,
%U 9338,11732,14627,15508,19314,23999,29654,31519,38907,47835,58555,62090,75942
%N Number of partitions of n having (sum of odd parts) < (sum of even parts).
%H Alois P. Heinz, <a href="/A239259/b239259.txt">Table of n, a(n) for n = 0..500</a>
%F a(n) + A239263(n) = A000041(n).
%e a(8) counts these 8 partitions: 8, 62, 611, 44, 422, 4211, 2222, 22211.
%t z = 40; p[n_] := p[n] = IntegerPartitions[n]; f[t_] := f[t] = Length[t]
%t t1 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] < n &]], {n, z}] (* A239259 *)
%t t2 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] <= n &]], {n, z}] (* A239260 *)
%t t3 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] == n &]], {n, z}] (* A239261 *)
%t t4 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] > n &]], {n, z}] (* A239262 *)
%t t5 = Table[f[Select[p[n], 2 Total[Select[#, OddQ]] >= n &]], {n, z}] (* A239263 *)
%t (* _Peter J. C. Moses_, Mar 12 2014 *)
%Y Cf. A239260, A239261, A239262, A239263, A000041.
%K nonn,easy
%O 0,5
%A _Clark Kimberling_, Mar 13 2014
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