A111295 Number of partitions of 3n+1.

1, 5, 15, 42, 101, 231, 490, 1002, 1958, 3718, 6842, 12310, 21637, 37338, 63261, 105558, 173525, 281589, 451276, 715220, 1121505, 1741630, 2679689, 4087968, 6185689, 9289091, 13848650, 20506255, 30167357, 44108109, 64112359, 92669720, 133230930, 190569292

Offset: 0

Author

Parthasarathy Nambi, Nov 01 2005

Keywords

• nonn

Comments

Old name was: P(3*n + 1) where P(m) is the unrestricted partition of m and n = 1,2,3,... .

a(n) is also the number of partitions of 4n-2 that include n as a part; see Comment at A000041. - Clark Kimberling, Mar 03 2014

Examples

			If n=25 then P(3*25 + 1) = 9289091.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000041, A016777, A058695.

Programs

Mathematica

Table[PartitionsP[3 n + 1], {n, 0, 10}]

PARI

a(n) = numbpart(3*n+1); \\ Michel Marcus, Mar 04 2014

Formula

a(n) = A000041(A016777(n)). - Michel Marcus, Sep 01 2021

Extensions

Better name from Clark Kimberling, Mar 02 2014