A241738 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

A241738

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).

3

1, 0, 0, 2, 1, 2, 7, 5, 7, 17, 14, 18, 39, 32, 42, 76, 71, 88, 157, 143, 182, 293, 292, 357, 562, 558, 692, 1023, 1060, 1286, 1854, 1932, 2347, 3246, 3464, 4153, 5639, 6030, 7207, 9526, 10324, 12240, 15912, 17311, 20444, 26104, 28585, 33567, 42326, 46469

(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..49.

FORMULA

a(n) + A241737(n) + A241839(n) = A000041(n) for n >= 0.

EXAMPLE

a(8) counts these 7 partitions: 5111, 422, 3221, 3211, 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[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, A241739, A241740, A241743.

Sequence in context: A011241 A261879 A167480 * A021051 A113246 A358604

Adjacent sequences: A241735 A241736 A241737 * A241739 A241740 A241741

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 28 2014

STATUS

approved