A014344 Four-fold convolution of primes with themselves.

16, 96, 376, 1160, 3121, 7532, 16754, 34796, 68339, 127952, 229956, 398688, 669781, 1094076, 1742710, 2713604, 4139111, 6195712, 9115304, 13199072, 18833449, 26509260, 36843322, 50603884, 68740107, 92414192, 123039628, 162323200, 212312453, 275448380

Offset

0,1

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

G.f.: ((1/x)*Sum_{k>=1} prime(k)*x^k)^4. - Ilya Gutkovskiy, Mar 10 2018

Maple

b:= proc(n, k) option remember; `if`(k=1, ithprime(n+1),
      add(b(j, floor(k/2))*b(n-j, ceil(k/2)), j=0..n))
    end:
a:= n-> b(n, 4):
seq(a(n), n=0..35);  # Alois P. Heinz, Mar 10 2018

Mathematica

b[n_, k_] := b[n, k] = If[k==1, Prime[n+1], Sum[b[j, Floor[k/2]] b[n-j, Ceiling[k/2]], {j, 0, n}]];
a[n_] := b[n, 4];
a /@ Range[0, 35] (* Jean-François Alcover, Nov 16 2020, after Alois P. Heinz *)

Prog

(PARI) my(N = 50, x = 'x + O('x^N)); Vec(((1/x)*sum(k=1, N, prime(k)*x^k))^4) \\ Michel Marcus, Mar 10 2018

Crossrefs

Cf. A000040, A014342, A014343.

Column k=4 of A340991.

Sequence in context: A143060 A006637 A241937 * A239613 A100313 A091079

Adjacent sequences: A014341 A014342 A014343 * A014345 A014346 A014347

Keyword

nonn

Author

N. J. A. Sloane

Status

approved