A241743 - OEIS

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

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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