A341481 Number of ways to write n as an ordered sum of 4 nonprime numbers.

1, 0, 0, 4, 0, 4, 6, 4, 16, 8, 18, 28, 25, 40, 50, 56, 76, 92, 98, 136, 147, 176, 212, 240, 272, 328, 352, 420, 471, 524, 592, 668, 747, 808, 938, 996, 1127, 1232, 1354, 1456, 1658, 1720, 1966, 2052, 2279, 2408, 2700, 2772, 3144, 3232, 3568, 3740, 4117, 4228, 4722

Offset: 4

Author

Ilya Gutkovskiy, Feb 13 2021

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 4..10000

Crossrefs

Cf. A005171, A018252, A052284, A076608, A340960, A341451, A341462, A341480, A341482, A341483, A341484, A341485, 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, 4):
seq(a(n), n=4..58);  # Alois P. Heinz, Feb 13 2021

Mathematica

nmax = 58; CoefficientList[Series[Sum[Boole[!PrimeQ[k]] x^k, {k, 1, nmax}]^4, {x, 0, nmax}], x] // Drop[#, 4] &

Formula

G.f. g(x)^4, where g(x) is the G.f. of A005171.