A087180 Number partition numbers <= P(n) of the form 3*k (P = A000041).

0, 0, 0, 1, 1, 1, 1, 2, 2, 3, 4, 4, 4, 4, 5, 5, 6, 7, 7, 7, 8, 9, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 14, 15, 15, 16, 16, 16, 16, 17, 18, 19, 19, 20, 20, 20, 21, 21, 22, 22, 22, 23, 24, 25, 25, 25, 25, 26, 26, 26, 26, 27, 27, 28, 28, 28, 28, 28, 29, 29, 30, 31, 31, 31, 31, 32

Offset: 0

Author

Reinhard Zumkeller, Aug 23 2003

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Partition Function.
• Eric Weisstein's World of Mathematics, Partition Function P Congruences.

Crossrefs

Cf. A000041, A068907, A071754, A087177, A087181, A087182, A087183.

Programs

Mathematica

Accumulate[Table[Boole[Mod[PartitionsP[n], 3] == 0], {n, 0, 100}]] (* Amiram Eldar, May 22 2025 *)

Formula

a(n) + A087181(n) + A087182(n) = n + 1.