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%I #25 Jul 28 2015 08:56:26
%S 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,
%T 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,
%U 0,0,0,0,1,0,0,0,0,0,0,0,0
%N Number of ways to write n as n = x! + y! + z! where 0<=x<=y<=z<=n.
%C If a(n) > 1 then a(n+1) = a(n) - 1.
%C If A034968(n) > 3 then a(n) = 0. - _David A. Corneth_, Jul 27 2015
%H David A. Corneth, <a href="/A071692/b071692.txt">Table of n, a(n) for n = 0..10000</a>
%p M:= 5: # for a(0) to a((M+1)!-1), where M >= 3
%p N:= (M+1)!-1:
%p A:= Array(0..N):
%p for x from 0 to M do for y from x to M do for z from y to M do
%p r:= x!+y!+z!;
%p A[r]:= A[r]+1;
%p od od od:
%p seq(A[i],i=0..N); # _Robert Israel_, Jul 27 2015
%o (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)))),","))
%o (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
%Y Cf. A034968.
%K easy,nonn
%O 0,4
%A _Benoit Cloitre_, Jun 23 2002
%E a(0)=0 prepended by _David A. Corneth_, Jul 28 2015
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