A241636 - OEIS

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A241636

Number of partitions p of n such that (number of even numbers in p) < (number of odd numbers in p).

6

0, 1, 1, 2, 2, 3, 5, 6, 10, 13, 21, 25, 40, 47, 69, 85, 118, 142, 192, 236, 310, 381, 485, 606, 761, 949, 1168, 1462, 1793, 2230, 2697, 3358, 4040, 4987, 5967, 7348, 8746, 10688, 12675, 15403, 18247, 22028, 25995, 31236, 36798, 43963, 51706, 61487, 72197

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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) + A241638(n) = A241637(n) for n >= 0.

a(n) + A241638(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 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_ /; 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. A241637, A241638, A241639, A241640.

Sequence in context: A227392 A050380 A241652 * A227360 A111077 A283189

Adjacent sequences: A241633 A241634 A241635 * A241637 A241638 A241639

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 27 2014

STATUS

approved