A341504 - OEIS

%I #6 Feb 13 2021 16:02:10

%S 1,0,0,10,0,10,45,10,100,130,135,460,390,820,1435,1552,3135,4090,5805,

%T 9370,12040,17890,25485,33940,48385,65812,87925,121040,160155,212350,

%U 283666,368590,482750,628390,806450,1039382,1327060,1682860,2134730,2684320,3364819

%N Number of ways to write n as an ordered sum of 10 nonprime numbers.

%p b:= proc(n, t) option remember;

%p       `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(

%p       `if`(isprime(j), 0, b(n-j, t-1)), j=1..n)))

%p     end:

%p a:= n-> b(n, 10):

%p seq(a(n), n=10..50);  # _Alois P. Heinz_, Feb 13 2021

%t nmax = 50; CoefficientList[Series[Sum[Boole[!PrimeQ[k]] x^k, {k, 1, nmax}]^10, {x, 0, nmax}], x] // Drop[#, 10] &

%Y Cf. A005171, A018252, A052284, A076608, A340966, A341460, A341469, A341480, A341481, A341482, A341483, A341484, A341485, A341486.

%K nonn

%O 10,4

%A _Ilya Gutkovskiy_, Feb 13 2021