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 A241653 Number of partitions p of n such that 2*(number of even numbers in p) = (number of odd numbers in p). 5
 1, 0, 0, 0, 0, 0, 1, 1, 4, 5, 11, 12, 24, 25, 42, 46, 70, 72, 106, 110, 156, 157, 212, 218, 291, 295, 383, 391, 516, 524, 679, 712, 931, 978, 1280, 1392, 1820, 2002, 2609, 2920, 3816, 4310, 5547, 6350, 8118, 9286, 11749, 13502, 16892, 19391, 23996, 27498 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 COMMENTS Each number in p is counted once, regardless of its multiplicity. LINKS FORMULA a(n) = A241652(n) - A241651(n) for n >= 0. a(n) + A241651(n) + A241655(n) = A000041(n) for n >= 0. EXAMPLE a(6) counts this single partition:  321. MATHEMATICA z = 30; f[n_] := f[n] = IntegerPartitions[n]; s0[p_] := Count[Mod[DeleteDuplicates[p], 2], 0]; s1[p_] := Count[Mod[DeleteDuplicates[p], 2], 1]; Table[Count[f[n], p_ /; 2 s0[p] < s1[p]], {n, 0, z}]  (* A241651 *) Table[Count[f[n], p_ /; 2 s0[p] <= s1[p]], {n, 0, z}] (* A241652 *) Table[Count[f[n], p_ /; 2 s0[p] == s1[p]], {n, 0, z}] (* A241653 *) Table[Count[f[n], p_ /; 2 s0[p] >= s1[p]], {n, 0, z}] (* A241654 *) Table[Count[f[n], p_ /; 2 s0[p] > s1[p]], {n, 0, z}]  (* A241655 *) CROSSREFS Cf. A241651, A241652, A241654, A241655. Sequence in context: A261673 A027708 A047374 * A100107 A066828 A163098 Adjacent sequences:  A241650 A241651 A241652 * A241654 A241655 A241656 KEYWORD nonn,easy AUTHOR Clark Kimberling, Apr 27 2014 STATUS approved

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Last modified September 23 20:42 EDT 2021. Contains 347617 sequences. (Running on oeis4.)