A341719 Number of partitions of n into 9 primes (counting 1 as a prime).

1, 1, 2, 2, 4, 4, 7, 7, 11, 11, 16, 15, 23, 21, 30, 27, 39, 35, 51, 44, 63, 54, 78, 67, 97, 81, 116, 96, 139, 115, 166, 133, 194, 155, 227, 180, 265, 206, 305, 236, 351, 271, 403, 305, 460, 346, 522, 391, 592, 438, 668, 489, 751, 551, 844, 608, 942, 674, 1050, 750

Offset

9,3

Links

Table of n, a(n) for n=9..68.

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)))(
     `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=9..68);  # 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]]][
     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, 9, 68}] (* Jean-François Alcover, Feb 26 2022, after Alois P. Heinz *)

Crossrefs

Cf. A008578, A034891, A259200, A341945, A341946, A341947, A341948, A341949, A341950, A341951, A341972.

Sequence in context: A060028 A341951 A182410 * A099770 A099383 A341972

Adjacent sequences: A341716 A341717 A341718 * A341720 A341721 A341722

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 24 2021

Status

approved