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URL: https://oeis.org/A241739

⇱ A241739 - OEIS

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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).

3

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

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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: A029628 A388590 A346159 * A226509 A329694 A183389

Adjacent sequences: A241736 A241737 A241738 * A241740 A241741 A241742

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 28 2014

STATUS

approved