A341461 Number of partitions of n into 3 distinct nonprime parts.

1, 0, 1, 1, 2, 1, 2, 2, 4, 3, 4, 4, 6, 5, 8, 7, 9, 9, 10, 12, 14, 14, 14, 17, 19, 19, 22, 23, 24, 28, 27, 31, 33, 35, 36, 40, 40, 44, 47, 49, 50, 55, 53, 61, 62, 66, 65, 73, 72, 79, 81, 86, 85, 95, 91, 101, 101, 109, 107, 119, 114, 125, 125, 134, 134

Offset

11,5

Links

Alois P. Heinz, Table of n, a(n) for n = 11..10000

Maple

b:= proc(n, i, t) option remember; `if`(n=0,
      `if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
      `if`(isprime(i), 0, b(n-i, min(n-i, i-1), t-1))))
    end:
a:= n-> b(n$2, 3):
seq(a(n), n=11..75);  # Alois P. Heinz, Feb 12 2021

Mathematica

b[n_, i_, t_] := b[n, i, t] = If[n == 0,
     If[t == 0, 1, 0], If[i < 1 || 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, 3];
a /@ Range[11, 75] (* Jean-François Alcover, Jul 01 2021, after Alois P. Heinz *)

Prog

(Python)
from functools import lru_cache
from sympy import isprime
@lru_cache(maxsize=None)
def b(n, i, t):
  if n == 0: return int(t == 0)
  if i < 1 or t < 1: return 0
  b2 = 0 if isprime(i) else b(n-i, min(n-i, i-1), t-1)
  return b(n, i-1, t) + b2
a = lambda n: b(n, n, 3)
print([a(n) for n in range(11, 76)]) # Michael S. Branicky, Feb 12 2021 after Alois P. Heinz

Crossrefs

Cf. A005171, A018252, A096258, A125688, A302479, A341408, A341462, A341464, A341465, A341466, A341467.

Sequence in context: A133770 A288310 A332718 * A337485 A328678 A184199

Adjacent sequences: A341458 A341459 A341460 * A341462 A341463 A341464

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 12 2021

Status

approved