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

3,1

Links

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

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 *)

Crossrefs

Column 3 of A180281.

Sequence in context: A224659 A034541 A180879 * A037765 A037653 A229665

Adjacent sequences: A180280 A180281 A180282 * A180284 A180285 A180286

Keyword

nonn

Author

R. H. Hardin, Aug 24 2010

Status

approved