|
| |
|
|
A023360
|
|
Number of compositions of n into prime parts.
|
|
30
|
|
|
|
1, 0, 1, 1, 1, 3, 2, 6, 6, 10, 16, 20, 35, 46, 72, 105, 152, 232, 332, 501, 732, 1081, 1604, 2352, 3493, 5136, 7595, 11212, 16534, 24442, 36039, 53243, 78573, 115989, 171264, 252754, 373214, 550863, 813251, 1200554, 1772207, 2616338, 3862121, 5701553
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,6
|
|
|
REFERENCES
|
S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 292-295.
Silvia Heubach and Toufik Mansour, Combinatorics of Compositions and Words, CRC Press, 2010.
|
|
|
LINKS
|
Alois P. Heinz, Table of n, a(n) for n = 0..2000 (first 501 terms from T. D. Noe)
S. R. Finch, Kalmar's composition constant, June 5, 2003. [Cached copy, with permission of the author]
Philippe Flajolet, More information including asymptotic form (1995). [Broken link]
P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; see page 43, 298
|
|
|
FORMULA
|
a(n) = Sum_{prime p<=n} a(n-p) with a(0)=1. - Henry Bottomley, Dec 15 2000
G.f.: 1/(1 - Sum_{k>=1} x^A000040(k)). - Andrew Howroyd, Dec 28 2017
|
|
|
EXAMPLE
|
2; 3; 4 = 2+2; 5 = 2+3 = 3+2; 6 = 2+2+2 = 3+3; 7 = 2+2+3 = 2+3+2 = 3+2+2 = 2+5 = 5+2; etc.
|
|
|
MAPLE
|
a:= proc(n) option remember; `if`(n=0, 1, add(
`if`(isprime(j), a(n-j), 0), j=1..n))
end:
seq(a(n), n=0..50); # Alois P. Heinz, Feb 12 2021
|
|
|
MATHEMATICA
|
CoefficientList[ Series[1 / (1 - Sum[ x^Prime[i], {i, 15}]), {x, 0, 45}], x]
|
|
|
PROG
|
(PARI) {my(n=60); Vec(1/(1-sum(k=1, n, if(isprime(k), x^k, 0))) + O(x*x^n))} \\ Andrew Howroyd, Dec 28 2017
|
|
|
CROSSREFS
|
Cf. A000607 for the unordered (partition) version.
Sequence in context: A064684 A098071 A286970 * A154028 A157793 A096375
Adjacent sequences: A023357 A023358 A023359 * A023361 A023362 A023363
|
|
|
KEYWORD
|
nonn,changed
|
|
|
AUTHOR
|
David W. Wilson
|
|
|
STATUS
|
approved
|
| |
|
|
