A365631 - OEIS

%I #22 Sep 16 2023 17:03:43

%S 1,2,5,10,20,36,58,95,147,222,323,462,636,889,1184,1584,2060,2686,

%T 3403,4353,5433,6768,8319,10230,12363,15011,17943,21467,25403,30044,

%U 35231,41294,48002,55718,64328,74086,84880,97071,110607,125692,142313,160728,181112,203438,228124

%N Number of partitions of n with exactly five part sizes.

%H Alois P. Heinz, <a href="/A365631/b365631.txt">Table of n, a(n) for n = 15..5000</a>

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

%e a(16) = 2 because we have 6+4+3+2+1, 5+4+3+2+1+1.

%p # Using function P from A365676:

%p A365631 := n -> P(n, 5, n): seq(A365631(n), n = 15..59); # _Peter Luschny_, Sep 15 2023

%o (Python)

%o from sympy.utilities.iterables import partitions

%o def A365631(n): return sum(1 for p in partitions(n) if len(p)==5) # _Chai Wah Wu_, Sep 14 2023

%Y A diagonal of A060177.

%Y Column k=5 of A116608.

%Y Cf. A000005, A002133, A002134, A365630.

%Y Cf. A364809.

%K nonn

%O 15,2

%A _Seiichi Manyama_, Sep 13 2023