A241745 Number of partitions p of n such that (number of numbers in p of form 3k) > (number of numbers in p of form 3k+1).

0, 0, 0, 1, 0, 1, 2, 1, 3, 4, 4, 8, 10, 13, 19, 24, 34, 45, 59, 79, 99, 130, 170, 212, 273, 348, 425, 546, 678, 833, 1041, 1284, 1558, 1940, 2351, 2862, 3496, 4227, 5093, 6187, 7409, 8920, 10706, 12795, 15277, 18259, 21671, 25803, 30579, 36218, 42836, 50596

Offset

0,7

Comments

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

Links

Table of n, a(n) for n=0..51.

Formula

a(n) + A241744(n) + A241845(n) = A000041(n) for n >= 0.

Example

a(8) counts these 3 partitions:  62, 53, 332.

Mathematica

z = 40; f[n_] := f[n] = IntegerPartitions[n]; s[k_, p_] := Count[Mod[DeleteDuplicates[p], 3], k];
Table[Count[f[n], p_ /; s[0, p] < s[2, p]], {n, 0, z}]  (* A241743 *)
Table[Count[f[n], p_ /; s[0, p] == s[1, p]], {n, 0, z}] (* A241744 *)
Table[Count[f[n], p_ /; s[0, p] > s[1, p]], {n, 0, z}]  (* A241745 *)

Crossrefs

Cf. A241737, A241740, A241743, A241744.

Sequence in context: A033799 A347494 A325324 * A332723 A210040 A349385

Adjacent sequences: A241742 A241743 A241744 * A241746 A241747 A241748

Keyword

nonn,easy

Author

Clark Kimberling, Apr 28 2014

Status

approved