A341980 Number of partitions of n into 9 distinct primes (counting 1 as a prime).

1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 3, 0, 1, 0, 3, 0, 5, 0, 4, 1, 6, 0, 10, 0, 6, 1, 11, 1, 16, 1, 11, 2, 19, 2, 25, 1, 18, 5, 32, 4, 36, 2, 32, 9, 47, 7, 55, 7, 49, 14, 69, 10, 80, 12, 74, 22, 98, 19, 117, 22, 106, 34, 140, 31, 158, 32, 149, 54, 194, 48, 215, 50

Offset

78,11

Links

Table of n, a(n) for n=78..151.

Maple

b:= proc(n, i) option remember; series(`if`(n=0, 1,
     `if`(i<0, 0, (p-> `if`(p>n, 0, x*b(n-p, i-1)))(
     `if`(i=0, 1, ithprime(i)))+b(n, i-1))), x, 10)
    end:
a:= n-> coeff(b(n, numtheory[pi](n)), x, 9):
seq(a(n), n=78..151);  # Alois P. Heinz, Feb 24 2021

Mathematica

b[n_, i_] := b[n, i] = Series[If[n == 0, 1,
     If[i < 0, 0, Function[p, If[p > n, 0, x*b[n - p, i - 1]]][
     If[i == 0, 1, Prime[i]]] + b[n, i - 1]]], {x, 0, 10}];
a[n_] := Coefficient[b[n, PrimePi[n]], x, 9];
Table[a[n], {n, 78, 151}] (* Jean-François Alcover, Feb 24 2022, after Alois P. Heinz *)

Crossrefs

Cf. A008578, A036497, A219203, A341719, A341973, A341974, A341975, A341976, A341977, A341978, A341979, A341981.

Sequence in context: A243016 A284975 A219202 * A218031 A135523 A194663

Adjacent sequences: A341977 A341978 A341979 * A341981 A341982 A341983

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 24 2021

Status

approved