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A241641 Number of partitions p of n such that (number of even numbers in p) < 2*(number of odd numbers in p). 5
0, 1, 1, 3, 3, 7, 8, 14, 16, 26, 32, 45, 57, 78, 103, 132, 175, 221, 299, 366, 491, 599, 803, 962, 1278, 1528, 2014, 2391, 3109, 3681, 4749, 5596, 7132, 8401, 10602, 12445, 15554, 18244, 22600, 26468, 32493, 38025, 46346, 54164, 65522, 76549, 92009, 107375 (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..47.

FORMULA

a(n) = A241642(n) - A241643(n) for n >= 0.

a(n) + A241643(n) + A241645(n) = A000041(n) for n >= 0.

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] < 2 s1[p]], {n, 0, z}]  (* A241641 *)

Table[Count[f[n], p_ /; s0[p] <= 2 s1[p]], {n, 0, z}] (* A241642 *)

Table[Count[f[n], p_ /; s0[p] == 2 s1[p]], {n, 0, z}] (* A241643 *)

Table[Count[f[n], p_ /; s0[p] >= 2 s1[p]], {n, 0, z}] (* A241644 *)

Table[Count[f[n], p_ /; s0[p] > 2 s1[p]], {n, 0, z}]  (* A241645 *)

CROSSREFS

Cf. A241642, A241643, A241644, A241645.

Sequence in context: A218567 A161416 A241637 * A339398 A241414 A218568

Adjacent sequences:  A241638 A241639 A241640 * A241642 A241643 A241644

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 27 2014

STATUS

approved

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Last modified May 19 18:35 EDT 2022. Contains 353847 sequences. (Running on oeis4.)