A241740 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, 0, 1, 1, 1, 3, 4, 4, 7, 10, 12, 17, 24, 30, 40, 53, 70, 90, 118, 152, 194, 244, 316, 396, 497, 626, 784, 960, 1202, 1483, 1816, 2230, 2738, 3312, 4042, 4908, 5922, 7141, 8627, 10327, 12388, 14832, 17703, 21075, 25120, 29795, 35321, 41822, 49439, 58286

Offset

0,7

Comments

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

Links

Table of n, a(n) for n=0..50.

Formula

a(n) + A241741(n) + A241842(n) = A000041(n) for n >= 0.

Example

a(8) counts these 4 partitions:  611, 431, 3311, 311111.

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, A241741, A241741, A241743.

Sequence in context: A231219 A231343 A121924 * A342332 A225738 A186679

Adjacent sequences: A241737 A241738 A241739 * A241741 A241742 A241743

Keyword

nonn,easy

Author

Clark Kimberling, Apr 28 2014

Status

approved