A071689 - OEIS

%I #11 Nov 20 2018 08:05:36

%S 1,1,2,3,4,6,7,9,10,13,15,17,19,23,24,29,31,35,37,42,45,50,53,57,62,

%T 69,71,77,81,87,92,99,102,111,116,122,128,138,140,148,156,165,170,180,

%U 184,195,203,210,218,229,236,246,254,263,271,285,291,304,311,322

%N Number of ways to write n as n = x*y*z*t+x+y+z+t 0<=x<=y<=z<=t<=n.

%H Jean-François Alcover, <a href="/A071689/b071689.txt">Table of n, a(n) for n = 0..199</a>

%t xmax = 3; ymax = 66; zmax = 99;(* When extending data, terms where maxima for x, y or z are reached have to be checked one by one. *)

%t r[n_] := r[n] = Module[{r1, r2, r3, rn}, r1 = Reap[Do[rn = Reduce[n == x y z t + x + y + z + t && 0 <= x <= y <= z <= t <= n, t, Integers]; If[rn =!= False, Sow[{x, y, z, t} /. {ToRules[rn]}]], {x, 0, xmax}, {y, 0, ymax}, {z, 0, zmax}]]; If[r1 == {Null, {}} , {}, r2 = r1[[2, 1]]; r3 = Flatten[r2, 1]; If[Max[r3[[All, 1]]] == xmax, Print["xmax reached at n = ", n]]; If[Max[r3[[All, 2]]] == ymax, Print["ymax reached at n = ", n]]; If[Max[r3[[All, 3]]] == zmax, Print["zmax reached at n = ", n]]; r3]];

%t a[n_] := Length[r[n]];

%t Table[Print[n, " ", a[n]]; a[n], {n, 0, m = 199}] (* _Jean-François Alcover_, Nov 20 2018 *)

%o (PARI) for(n=0,50,print1(sum(a=0,n,sum(b=0,a,sum(c=0,b,sum(d=0,c,if(a*b*c*d+a+b+c+d-n,0,1))))),","))

%Y Cf. A260803, A260804.

%K easy,nonn

%O 0,3

%A _Benoit Cloitre_, Jun 23 2002