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A341462 Number of partitions of n into 4 distinct nonprime parts. 8
1, 1, 1, 1, 2, 2, 3, 3, 5, 5, 7, 6, 10, 9, 13, 12, 17, 17, 21, 21, 28, 28, 34, 33, 42, 43, 51, 53, 61, 63, 73, 76, 87, 91, 102, 104, 119, 123, 137, 143, 157, 164, 179, 187, 205, 215, 232, 239, 262, 272, 294, 309, 327, 341, 365, 381, 406, 427, 448, 465 (list; graph; refs; listen; history; text; internal format)
OFFSET

19,5

LINKS

Table of n, a(n) for n=19..78.

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, 4):

seq(a(n), n=19..78);  # 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, 4];

Table[a[n], {n, 19, 78}] (* Jean-Fran├žois Alcover, Jul 13 2021, after Alois P. Heinz *)

Table[Length[Select[IntegerPartitions[n, {4}], Length[#]==Length[ Union[ #]] && NoneTrue[#, PrimeQ]&]], {n, 19, 80}] (* Harvey P. Dale, Nov 07 2021 *)

CROSSREFS

Cf. A005171, A018252, A096258, A219198, A302479, A341451, A341461, A341464, A341465, A341466, A341467.

Sequence in context: A086609 A341140 A340285 * A035031 A035032 A121260

Adjacent sequences:  A341459 A341460 A341461 * A341463 A341464 A341465

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Feb 12 2021

STATUS

approved

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Last modified November 29 04:15 EST 2021. Contains 349416 sequences. (Running on oeis4.)