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A241654 Number of partitions p of n such that 2*(number of even numbers in p) = (number of odd numbers in p). 5
1, 0, 1, 1, 3, 4, 7, 10, 16, 22, 32, 43, 61, 79, 108, 138, 184, 231, 304, 378, 491, 605, 775, 954, 1212, 1485, 1868, 2283, 2856, 3477, 4315, 5246, 6473, 7839, 9613, 11618, 14167, 17054, 20688, 24827, 29984, 35847, 43073, 51337, 61425, 72939, 86905, 102871 (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..47.

FORMULA

a(n) = A241653(n) + A241655(n) for n >= 0.

a(n) + A241651(n) + A241655(n) = A000041(n) for n >= 0.

EXAMPLE

a(6) counts these 7 partitions:  6, 42, 411, 321, 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, A241655.

Sequence in context: A275633 A004397 A324368 * A047967 A282893 A256912

Adjacent sequences:  A241651 A241652 A241653 * A241655 A241656 A241657

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 27 2014

STATUS

approved

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Last modified July 25 02:17 EDT 2021. Contains 346273 sequences. (Running on oeis4.)