A241742 Number of partitions p of n such that (number of numbers in p of form 3k+2) > (number of numbers in p of form 3k).

0, 0, 1, 1, 2, 3, 5, 6, 9, 12, 18, 22, 31, 41, 54, 70, 95, 120, 156, 202, 259, 325, 418, 524, 659, 826, 1032, 1274, 1581, 1949, 2397, 2932, 3592, 4367, 5307, 6430, 7783, 9370, 11288, 13550, 16233, 19399, 23179, 27579, 32812, 38955, 46155, 54572, 64524, 76051

Offset

0,5

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) + A241740(n) + A241841(n) = A000041(n) for n >= 0.

Example

a(8) counts these 9 partitions:  8, 521, 5111, 422, 4211, 2222, 22211, 221111, 2111111.

Mathematica

z = 40; f[n_] := f[n] = IntegerPartitions[n]; s[k_, p_] := Count[Mod[DeleteDuplicates[p], 3], k];
Table[Count[f[n], p_ /; s[2, p] < s[0, p]], {n, 0, z}]  (* A241740 *)
Table[Count[f[n], p_ /; s[2, p] == s[0, p]], {n, 0, z}] (* A241741 *)
Table[Count[f[n], p_ /; s[2, p] > s[0, p]], {n, 0, z}]  (* A241742 *)

Crossrefs

Cf. A241737, A241740, A241741, A241743.

Sequence in context: A035948 A258939 A244747 * A212584 A330228 A166048

Adjacent sequences: A241739 A241740 A241741 * A241743 A241744 A241745

Keyword

nonn,easy

Author

Clark Kimberling, Apr 28 2014

Status

approved