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%I #9 Feb 24 2024 10:50:23
%S 1,1,1,1,2,2,3,4,5,7,7,7,10,9,10,12,14,15,16,16,18,19,19,20,22,23,23,
%T 25,26,27,27,28,30,31,31,33,34,35,36,37,38,39,40,40,41,42,43,45,46,47,
%U 48,49,50,51,52,53,54,55,56,57,56,58,60,61,62,63,64,65,65
%N Number of distinct nonzero numbers of partitions of n counted by length.
%C Also the number of distinct nonzero entries in row n of A008284.
%e Row n = 9 of A008284 is (1, 4, 7, 6, 5, 3, 2, 1, 1), which has union {1,2,3,4,5,6,7}, so a(9) = 7.
%p b:= proc(n, i) option remember; `if`(n=0 or i=1, x^n,
%p b(n, i-1)+expand(x*b(n-i, min(n-i, i))))
%p end:
%p a:= n-> nops({coeffs(b(n$2))}):
%p seq(a(n), n=0..90); # _Alois P. Heinz_, Feb 23 2024
%t Table[Length[Union[Table[Length[IntegerPartitions[n,{k}]],{k,n}]]],{n,30}]
%Y Cf. A001221, A006128, A007870, A008284, A056239, A116608, A181819, A302247.
%K nonn
%O 0,5
%A _Gus Wiseman_, May 07 2019
%E a(0)=1 prepended by _Alois P. Heinz_, Feb 23 2024
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