A365630 Number of partitions of n with exactly four part sizes.

1, 2, 5, 10, 20, 30, 52, 77, 117, 162, 227, 309, 414, 535, 692, 873, 1100, 1369, 1661, 2030, 2438, 2925, 3450, 4108, 4759, 5570, 6440, 7457, 8491, 9798, 11020, 12593, 14125, 15995, 17820, 20074, 22182, 24833, 27379, 30422, 33351, 36996, 40346, 44445, 48336, 53048, 57494

Offset: 10

Author

Seiichi Manyama, Sep 13 2023

Keywords

• nonn

Examples

			a(11) = 2 because we have 5+3+2+1, 4+3+2+1+1.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 10..10000

Crossrefs

A diagonal of A060177.

Column k=4 of A116608.

Cf. A000005, A002133, A002134, A365631.

Programs

Maple

# Using function P from A365676:
A365630 := n -> P(n, 4, n): seq(A365630(n), n = 10..56); # Peter Luschny, Sep 15 2023

Python

from sympy.utilities.iterables import partitions
def A365630(n): return sum(1 for p in partitions(n) if len(p)==4) # Chai Wah Wu, Sep 14 2023

Formula

G.f.: Sum_{0

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.