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A241642 Number of partitions p of n such that (number of even numbers in p) <= 2*(number of odd numbers in p). 5
1, 1, 1, 3, 3, 7, 8, 15, 17, 30, 35, 56, 66, 100, 119, 172, 206, 286, 346, 464, 565, 739, 906, 1158, 1424, 1789, 2208, 2730, 3374, 4128, 5101, 6173, 7618, 9148, 11276, 13446, 16514, 19595, 24001, 28321, 34558, 40636, 49394, 57864, 70036, 81817, 98645, 114912 (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) = A241641(n) + A241643(n) for n >= 0.

a(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. A241641, A241643, A241644, A241645.

Sequence in context: A218572 A218573 A117989 * A086543 A281616 A110618

Adjacent sequences:  A241639 A241640 A241641 * A241643 A241644 A241645

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 27 2014

STATUS

approved

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Last modified May 28 04:02 EDT 2022. Contains 354112 sequences. (Running on oeis4.)