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A241655 Number of partitions p of n such that 2*(number of even numbers in p) = (number of odd numbers in p). 5
0, 0, 1, 1, 3, 4, 6, 9, 12, 17, 21, 31, 37, 54, 66, 92, 114, 159, 198, 268, 335, 448, 563, 736, 921, 1190, 1485, 1892, 2340, 2953, 3636, 4534, 5542, 6861, 8333, 10226, 12347, 15052, 18079, 21907, 26168, 31537, 37526, 44987, 53307, 63653, 75156, 89369, 105204 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Each number in p is counted once, regardless of its multiplicity.

LINKS

Table of n, a(n) for n=0..48.

FORMULA

a(n) = A241654(n) - A241653(n) for n >= 0.

a(n) + A241651(n) + A241653(n) = A000041(n) for n >= 0.

EXAMPLE

a(6) counts these 6 partitions:  6, 42, 411, 222, 2211, 21111.

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, A241653, A241654.

Sequence in context: A097922 A103109 A241639 * A288346 A078743 A096846

Adjacent sequences:  A241652 A241653 A241654 * A241656 A241657 A241658

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 27 2014

STATUS

approved

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Last modified September 17 07:51 EDT 2021. Contains 347478 sequences. (Running on oeis4.)