The On-Line Encyclopedia of Integer Sequences (OEIS)

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A243940

Number of partitions of n^2 into exactly 4 prime numbers.
(history; published version)

#10 by Bruno Berselli at Wed Apr 15 10:02:23 EDT 2015

STATUS

proposed

approved

#9 by Jean-François Alcover at Wed Apr 15 09:59:49 EDT 2015

STATUS

editing

proposed

#8 by Jean-François Alcover at Wed Apr 15 09:59:42 EDT 2015

MATHEMATICA

$RecursionLimit = 1000; b[n_, i_, t_] := b[n, i, t] = If[n == 0, If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] + Function[{p}, If[p > n, 0, b[n - p, i, t - 1]]][Prime[i]]]]; a[n_] := b[n^2, PrimePi[n^2], 4]; Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Apr 15 2015, after Alois P. Heinz *)

STATUS

approved

editing

#7 by Alois P. Heinz at Mon Jun 16 08:48:32 EDT 2014

STATUS

editing

approved

#6 by Alois P. Heinz at Mon Jun 16 08:48:27 EDT 2014

LINKS

Alois P. Heinz, <a href="/A243940/b243940.txt">Table of n, a(n) for n = 1..100</a>

#5 by Alois P. Heinz at Sun Jun 15 19:48:01 EDT 2014

MAPLE

with(numtheory):

b:= proc(n, i, t) option remember; `if`(n=0, `if`(t=0, 1, 0),

`if`(i<1 or t<1, 0, b(n, i-1, t) +(p-> `if`(p>n, 0,

b(n-p, i, t-1)))(ithprime(i))))

end:

a:= n-> b(n^2, pi(n^2), 4):

seq(a(n), n=1..40); # Alois P. Heinz, Jun 15 2014

#4 by Alois P. Heinz at Sun Jun 15 19:44:56 EDT 2014

NAME

Partitions Number of partitions of n^2 into exactly 4 prime numbers.

DATA

0, 0, 1, 3, 5, 15, 13, 50, 24, 126, 50, 258, 78, 508, 115, 899, 176, 1562, 240, 2383, 299, 3616, 440, 5733, 547, 7585, 664, 10705, 863, 16259, 1033, 19591, 1234, 25943, 1566, 37879, 1860, 43405, 1976, 55700, 2529, 78989, 2942, 86261, 3162, 106212, 3867, 148771

STATUS

proposed

editing

#3 by Olivier Gérard at Sun Jun 15 15:14:39 EDT 2014

STATUS

editing

proposed

#2 by Olivier Gérard at Sun Jun 15 15:11:41 EDT 2014

NAME

allocated for Olivier Gérard

Partitions of n^2 into exactly 4 prime numbers.

DATA

OFFSET

1,4

KEYWORD

allocated

nonn

AUTHOR

Olivier Gérard, Jun 15 2014

STATUS

approved

editing

#1 by Olivier Gérard at Sun Jun 15 15:11:41 EDT 2014

NAME

allocated for Olivier Gérard

KEYWORD

allocated

STATUS

approved