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%I #7 Sep 14 2021 08:56:16
%S 1,1,1,1,2,2,4,6,5,10,14,15,24,21,35,45,48,65,77,89,114,129,148,184,
%T 205,239,285,310,361,410,459,522,593,636,740,804,911,969,1123,1169,
%U 1350,1428,1595,1687,1926,1974,2270,2325,2611,2726,3064,3120,3547,3596,4012,4155
%N Number of compositions (ordered partitions) of n into at most 4 nonprime parts.
%t Table[Length@Flatten[Permutations/@IntegerPartitions[n,4,Select[Range@n,!PrimeQ@#&]],1],{n,0,55}] (* _Giorgos Kalogeropoulos_, Sep 14 2021 *)
%Y Cf. A018252, A052284, A341481, A347788, A347796, A347798, A347799.
%K nonn
%O 0,5
%A _Ilya Gutkovskiy_, Sep 14 2021