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A241637 Number of partitions p of n such that (number of even numbers in p) <= (number of odd numbers in p). 6
1, 1, 1, 3, 3, 7, 8, 14, 16, 26, 32, 45, 57, 78, 103, 132, 174, 220, 295, 361, 477, 584, 766, 921, 1194, 1436, 1841, 2207, 2782, 3331, 4169, 4981, 6156, 7373, 9019, 10778, 13093, 15636, 18843, 22507, 26920, 32096, 38205, 45470, 53845, 63970, 75377, 89356 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

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

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = A241636(n) + A241638(n) for n >= 0.

a(n) + A241640(n) = A000041(n) for n >= 0.

a(n) = Sum_{k>=0} A242618(n,k). - Alois P. Heinz, May 19 2014

EXAMPLE

a(6) counts these 8 partitions:  51, 411, 33, 321, 3111, 2211, 21111, 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_ /; s0[p] < s1[p]], {n, 0, z}]  (* A241636 *)

Table[Count[f[n], p_ /; s0[p] <= s1[p]], {n, 0, z}] (* A241637 *)

Table[Count[f[n], p_ /; s0[p] == s1[p]], {n, 0, z}] (* A241638 *)

Table[Count[f[n], p_ /; s0[p] >= s1[p]], {n, 0, z}] (* A241639 *)

Table[Count[f[n], p_ /; s0[p] > s1[p]], {n, 0, z}]  (* A241640 *)

CROSSREFS

Cf. A241636, A241638, A241639, A241640.

Sequence in context: A200792 A218567 A161416 * A241641 A241414 A218568

Adjacent sequences:  A241634 A241635 A241636 * A241638 A241639 A241640

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 27 2014

STATUS

approved

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Last modified January 19 15:37 EST 2020. Contains 331049 sequences. (Running on oeis4.)