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%I #4 May 03 2014 16:53:39
%S 1,0,0,0,0,0,1,1,4,5,11,12,24,25,42,46,70,72,106,110,156,157,212,218,
%T 291,295,383,391,516,524,679,712,931,978,1280,1392,1820,2002,2609,
%U 2920,3816,4310,5547,6350,8118,9286,11749,13502,16892,19391,23996,27498
%N Number of partitions p of n such that 2*(number of even numbers in p) = (number of odd numbers in p).
%C Each number in p is counted once, regardless of its multiplicity.
%F a(n) = A241652(n) - A241651(n) for n >= 0.
%F a(n) + A241651(n) + A241655(n) = A000041(n) for n >= 0.
%e a(6) counts this single partition: 321.
%t z = 30; f[n_] := f[n] = IntegerPartitions[n]; s0[p_] := Count[Mod[DeleteDuplicates[p], 2], 0];
%t s1[p_] := Count[Mod[DeleteDuplicates[p], 2], 1];
%t Table[Count[f[n], p_ /; 2 s0[p] < s1[p]], {n, 0, z}] (* A241651 *)
%t Table[Count[f[n], p_ /; 2 s0[p] <= s1[p]], {n, 0, z}] (* A241652 *)
%t Table[Count[f[n], p_ /; 2 s0[p] == s1[p]], {n, 0, z}] (* A241653 *)
%t Table[Count[f[n], p_ /; 2 s0[p] >= s1[p]], {n, 0, z}] (* A241654 *)
%t Table[Count[f[n], p_ /; 2 s0[p] > s1[p]], {n, 0, z}] (* A241655 *)
%Y Cf. A241651, A241652, A241654, A241655.
%K nonn,easy
%O 0,9
%A _Clark Kimberling_, Apr 27 2014
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