A241739 Number of partitions p of n such that (number of numbers in p of form 3k+1) > (number of numbers in p of form 3k+2).

0, 1, 1, 1, 3, 3, 3, 8, 9, 10, 20, 24, 27, 49, 58, 69, 109, 132, 153, 234, 279, 331, 469, 565, 662, 918, 1093, 1290, 1723, 2056, 2411, 3165, 3751, 4411, 5656, 6700, 7839, 9932, 11707, 13699, 17084, 20099, 23441, 28939, 33914, 39498, 48236, 56392, 65481

Offset

0,5

Comments

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

Links

Table of n, a(n) for n=0..48.

Formula

a(n) + A241737(n) + A241838(n) = A000041(n) for n >= 0.

Example

a(8) counts these 9 partitions: 71, 611, 44, 431, 4211, 3311, 311111, 11111111.

Mathematica

z = 40; f[n_] := f[n] = IntegerPartitions[n]; s[k_, p_] := Count[Mod[DeleteDuplicates[p], 3], k];
Table[Count[f[n], p_ /; s[1, p] < s[2, p]], {n, 0, z}]  (* A241737 *)
Table[Count[f[n], p_ /; s[1, p] == s[2, p]], {n, 0, z}] (* A241738 *)
Table[Count[f[n], p_ /; s[1, p] > s[2, p]], {n, 0, z}]  (* A241739 *)

Crossrefs

Cf. A241737, A241738, A241740, A241743.

Sequence in context: A177937 A029628 A346159 * A226509 A329694 A183389

Adjacent sequences: A241736 A241737 A241738 * A241740 A241741 A241742

Keyword

nonn,easy

Author

Clark Kimberling, Apr 28 2014

Status

approved