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%I #21 Sep 15 2023 18:41:41
%S 1,2,5,10,20,30,52,77,117,162,227,309,414,535,692,873,1100,1369,1661,
%T 2030,2438,2925,3450,4108,4759,5570,6440,7457,8491,9798,11020,12593,
%U 14125,15995,17820,20074,22182,24833,27379,30422,33351,36996,40346,44445,48336,53048,57494
%N Number of partitions of n with exactly four part sizes.
%H Alois P. Heinz, <a href="/A365630/b365630.txt">Table of n, a(n) for n = 10..10000</a>
%F 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) ).
%e a(11) = 2 because we have 5+3+2+1, 4+3+2+1+1.
%p # Using function P from A365676:
%p A365630 := n -> P(n, 4, n): seq(A365630(n), n = 10..56); # _Peter Luschny_, Sep 15 2023
%o (Python)
%o from sympy.utilities.iterables import partitions
%o def A365630(n): return sum(1 for p in partitions(n) if len(p)==4) # _Chai Wah Wu_, Sep 14 2023
%Y A diagonal of A060177.
%Y Column k=4 of A116608.
%Y Cf. A000005, A002133, A002134, A365631.
%K nonn
%O 10,2
%A _Seiichi Manyama_, Sep 13 2023
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