A341468 -id:A341468 - cp's OEIS frontend

A341486 Number of ways to write n as an ordered sum of 9 nonprime numbers.

1, 0, 0, 9, 0, 9, 36, 9, 81, 93, 108, 333, 270, 585, 945, 1047, 2016, 2547, 3612, 5571, 7101, 10227, 14256, 18621, 25830, 34497, 44955, 60610, 78480, 101754, 133092, 169380, 217008, 276852, 347967, 439272, 549786, 683244, 849528, 1047678, 1288017, 1577934

Offset: 9

Ilya Gutkovskiy, Feb 13 2021

nonn

Cf. A005171, A018252, A052284, A076608, A340965, A341457, A341468, A341480, A341481, A341482, A341483, A341484, A341485.

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, 9):
seq(a(n), n=9..50);  # Alois P. Heinz, Feb 13 2021

nmax = 50; CoefficientList[Series[Sum[Boole[!PrimeQ[k]] x^k, {k, 1, nmax}]^9, {x, 0, nmax}], x] // Drop[#, 9] &

A341469 Number of partitions of n into 10 distinct nonprime parts.

Original entry on oeis.org

1, 0, 1, 1, 2, 2, 4, 3, 6, 7, 10, 11, 17, 17, 25, 28, 38, 44, 57, 64, 82, 95, 117, 136, 168, 189, 231, 264, 317, 366, 433, 490, 579, 660, 770, 877, 1019, 1146, 1327, 1497, 1720, 1940, 2215, 2481, 2825, 3165, 3583, 4008, 4523, 5033, 5664

Offset: 95

Ilya Gutkovskiy, Feb 12 2021

nonn

Cf. A005171, A018252, A096258, A219204, A302479, A341460, A341461, A341462, A341464, A341465, A341466, A341467, A341468.

b:= proc(n, i, t) option remember; `if`(n=0,
      `if`(t=0, 1, 0), `if`(i b(n$2, 10):
seq(a(n), n=95..145);  # Alois P. Heinz, Feb 12 2021

b[n_, i_, t_] := b[n, i, t] = If[n == 0,
     If[t == 0, 1, 0], If[i < t || t < 1, 0, b[n, i - 1, t] +
     If[PrimeQ[i], 0, b[n - i, Min[n - i, i - 1], t - 1]]]];
a[n_] := b[n, n, 10];
Table[a[n], {n, 95, 145}] (* Jean-François Alcover, Feb 28 2022, after Alois P. Heinz *)

cp's OEIS Frontend

A341486 Number of ways to write n as an ordered sum of 9 nonprime numbers.

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