A087181 Number partition numbers <= P(n) of the form 3*k+1 (P = A000041).

1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 9, 9, 9, 9, 9, 9, 10, 10, 11, 12, 12, 12, 12, 12, 12, 12, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 16, 17, 17, 17, 17, 18, 18, 18, 19, 19, 20, 20, 20, 20, 20, 20, 20, 20, 21, 22, 22, 22, 22, 23, 23, 23

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, A087180, A087182, A087184.

Programs

Mathematica

Accumulate[Table[Boole[Mod[PartitionsP[n], 3] == 1], {n, 0, 100}]] (* Amiram Eldar, May 22 2025 *)

Formula

A087180(n) + a(n) + A087182(n) = n + 1.