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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

Table of n, a(n) for n=0..51.

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 July 5 19:02 EDT 2020. Contains 335473 sequences. (Running on oeis4.)