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

10,2

Links

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

Formula

G.f.: Sum_{0<i<j<k<l} x^(i+j+k+l)/( (1-x^i)*(1-x^j)*(1-x^k)*(1-x^l) ).

Example

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

Maple

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

Prog

(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

Crossrefs

A diagonal of A060177.

Column k=4 of A116608.

Cf. A000005, A002133, A002134, A365631.

Sequence in context: A000099 A039690 A243938 * A126105 A117486 A263002

Adjacent sequences: A365627 A365628 A365629 * A365631 A365632 A365633

Keyword

nonn

Author

Seiichi Manyama, Sep 13 2023

Status

approved