A241743 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, 1, 1, 2, 3, 4, 6, 8, 12, 16, 21, 30, 40, 52, 72, 91, 121, 159, 202, 260, 335, 421, 535, 674, 840, 1052, 1304, 1614, 1996, 2451, 3002, 3674, 4468, 5442, 6592, 7971, 9624, 11584, 13898, 16691, 19947, 23823, 28410, 33782, 40113, 47610, 56302, 66572, 78569

Offset

0,4

Comments

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

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

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

Example

a(8) counts these 12 partitions: 71, 521, 5111, 44, 431, 422, 4211, 41111, 22211, 221111, 2111111, 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[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, A241744, A241745.

Sequence in context: A261205 A036451 A297216 * A321729 A180652 A046682

Adjacent sequences: A241740 A241741 A241742 * A241744 A241745 A241746

Keyword

nonn,easy

Author

Clark Kimberling, Apr 28 2014

Status

approved