A180283 Number of arrangements of n indistinguishable balls in n boxes with the maximum number of balls in any box equal to 3.

3, 12, 50, 195, 735, 2716, 9912, 35850, 128865, 461175, 1645215, 5855941, 20810153, 73870748, 262029364, 929031504, 3293120337, 11672207262, 41373395052, 146674116501, 520093043437, 1844704839175, 6544970763175, 23229252652125

Offset: 3

Author

R. H. Hardin, Aug 24 2010

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 3..1795 (n=3..59 from R. H. Hardin)

Crossrefs

Column 3 of A180281.

Programs

Maple

f:= proc(m,n) option remember;
  if m > 3*n or m < 3 then return 0 fi;
  g(m-3,n-1) + add(procname(m-i,n-1),i=0..2)
end proc:
g:= proc(m,n) option remember;
  if m > 3*n then return 0 fi;
  add(procname(m-i,n-1), i=0..min(m,3))
end proc:
g(0,0):= 1:
seq(f(n,n),n=3..30); # Robert Israel, May 03 2018

Mathematica

b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i == 0, 0, Sum[b[n-j, i-1, k], {j, 0, Min[n, k]}]]];
a[n_] := b[n, n, 3] - b[n, n, 2];
Table[a[n], {n, 3, 30}] (* Jean-François Alcover, Aug 28 2022, after Alois P. Heinz in A180281 *)