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Number of compositions (ordered partitions) of n into at most 6 prime parts.
6

%I #8 Sep 12 2021 09:50:21

%S 1,0,1,1,1,3,2,6,6,10,16,20,35,46,71,98,130,182,226,295,359,430,534,

%T 626,746,880,1019,1196,1392,1574,1815,2063,2313,2655,2941,3275,3669,

%U 4017,4441,4917,5295,5852,6365,6957,7575,8198,8839,9511,10374,10958,11931

%N Number of compositions (ordered partitions) of n into at most 6 prime parts.

%F a(n) = Sum_{k=1..6} A121303(n,k) for n >= 2. - _Alois P. Heinz_, Sep 11 2021

%t Table[Length@Flatten[Permutations/@IntegerPartitions[n,6,Prime@Range@PrimePi@n],1],{n,0,50}] (* _Giorgos Kalogeropoulos_, Sep 12 2021 *)

%Y Cf. A000040, A023360, A121303, A340962, A347739, A347740, A347741, A347742.

%K nonn

%O 0,6

%A _Ilya Gutkovskiy_, Sep 11 2021