A002220 a(n) is the number of partitions of 3n that can be obtained by adding together three (not necessarily distinct) partitions of n.

1, 4, 10, 30, 65, 173, 343, 778, 1518, 3088, 5609, 10959, 18990, 34441, 58903, 102044, 167499, 282519, 451529, 737208, 1160102, 1836910, 2828466, 4410990, 6670202, 10161240, 15186315, 22758131, 33480869

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Examples

			From _Gus Wiseman_, Apr 20 2024: (Start)
The a(1) = 1 through a(3) = 10 triquanimous partitions:
  (111)  (222)     (333)
         (2211)    (3321)
         (21111)   (32211)
         (111111)  (33111)
                   (222111)
                   (321111)
                   (2211111)
                   (3111111)
                   (21111111)
                   (111111111)
(End)
		

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• N. Metropolis and P. R. Stein, An elementary solution to a problem in restricted partitions, J. Combin. Theory, 9 (1970), 365-376.

Crossrefs

See A002219 for further details. Cf. A002221, A002222, A213074.

A column of A213086.

For biquanimous we have A002219, ranks A357976.

For non-biquanimous we have A371795, ranks A371731, even case A006827.

The Heinz numbers of these partitions are given by A371955.

The strict case is A372122.

A321451 counts non-quanimous partitions, ranks A321453.

A321452 counts quanimous partitions, ranks A321454.

A371783 counts k-quanimous partitions.

Cf. A035470, A064914, A237258, A321142, A371737, A371792, A371796.

Extensions

Edited by N. J. A. Sloane, Jun 03 2012

a(12)-a(20) from Alois P. Heinz, Jul 10 2012

a(21)-a(29) from Sean A. Irvine, Sep 05 2013