login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 3 22:32 EST 2021. Contains 349468 sequences. (Running on oeis4.)