A071692 Number of ways to write n as n = x! + y! + z! where 0<=x<=y<=z<=n.

0, 0, 0, 4, 3, 2, 1, 0, 3, 2, 1, 0, 0, 2, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 2, 1, 0, 0, 2, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0

Offset

0,4

Comments

If a(n) > 1 then a(n+1) = a(n) - 1.

If A034968(n) > 3 then a(n) = 0. - David A. Corneth, Jul 27 2015

Links

David A. Corneth, Table of n, a(n) for n = 0..10000

Maple

M:= 5: # for a(0) to a((M+1)!-1), where M >= 3
N:= (M+1)!-1:
A:= Array(0..N):
for x from 0 to M do for y from x to M do for z from y to M do
   r:= x!+y!+z!;
   A[r]:= A[r]+1;
od od od:
seq(A[i], i=0..N); # Robert Israel, Jul 27 2015

Prog

(PARI) for(n=1, 80, print1(sum(a=0, n, sum(b=0, a, sum(c=0, b, if(a!+b!+c!-n, 0, 1)))), ", "))
(PARI) a(n) = {my(f=1, t=0); while((f+1)!<=n, f++); forvec(u=vector(3, i, [0, f]), t+=(sum(i=1, 3, u[i]!)==n), 1); t} \\ David A. Corneth, Jul 27 2015

Crossrefs

Cf. A034968.

Sequence in context: A258447 A066440 A182425 * A307335 A030586 A249345

Adjacent sequences: A071689 A071690 A071691 * A071693 A071694 A071695

Keyword

easy,nonn

Author

Benoit Cloitre, Jun 23 2002

Extensions

a(0)=0 prepended by David A. Corneth, Jul 28 2015

Status

approved