A341485 Number of ways to write n as an ordered sum of 8 nonprime numbers.

1, 0, 0, 8, 0, 8, 28, 8, 64, 64, 84, 232, 182, 400, 596, 680, 1232, 1520, 2128, 3144, 3970, 5504, 7532, 9584, 12945, 16920, 21464, 28288, 35778, 45264, 57856, 72024, 90036, 112456, 138140, 170600, 208874, 254192, 309088, 373584, 449731, 539408, 645584, 767776

Offset: 8

Author

Ilya Gutkovskiy, Feb 13 2021

Keywords

• nonn

Crossrefs

Cf. A005171, A018252, A052284, A076608, A340964, A341455, A341467, A341480, A341481, A341482, A341483, A341484, A341486.

Programs

Maple

b:= proc(n, t) option remember;
      `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(
      `if`(isprime(j), 0, b(n-j, t-1)), j=1..n)))
    end:
a:= n-> b(n, 8):
seq(a(n), n=8..51);  # Alois P. Heinz, Feb 13 2021

Mathematica

nmax = 51; CoefficientList[Series[Sum[Boole[!PrimeQ[k]] x^k, {k, 1, nmax}]^8, {x, 0, nmax}], x] // Drop[#, 8] &