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A241652 Number of partitions p of n such that 2*(number of even numbers in p) <= (number of odd numbers in p). 5
1, 1, 1, 2, 2, 3, 5, 6, 10, 13, 21, 25, 40, 47, 69, 84, 117, 138, 187, 222, 292, 344, 439, 519, 654, 768, 951, 1118, 1378, 1612, 1968, 2308, 2807, 3282, 3977, 4657, 5630, 6585, 7936, 9278, 11170, 13046, 15648, 18274, 21868, 25481, 30402, 35385, 42069, 48875 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

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

LINKS

Table of n, a(n) for n=0..49.

FORMULA

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

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

EXAMPLE

a(6) counts these 5 partitions:  51, 33, 321, 3111, 111111.

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, A241653, A241654, A241655.

Sequence in context: A160235 A227392 A050380 * A241636 A227360 A111077

Adjacent sequences:  A241649 A241650 A241651 * A241653 A241654 A241655

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 27 2014

STATUS

approved

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Last modified September 25 17:14 EDT 2021. Contains 347659 sequences. (Running on oeis4.)