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A014344
Four-fold convolution of primes with themselves.
2
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
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
Column k=4 of A340991.
Sequence in context: A143060 A006637 A241937 * A239613 A100313 A091079
KEYWORD
nonn
STATUS
approved