A180284 Number of arrangements of n indistinguishable balls in n boxes with the maximum number of balls in any box equal to 4.

4, 20, 90, 392, 1652, 6804, 27600, 110715, 440374, 1740024, 6838832, 26762645, 104356980, 405706292, 1573256772, 6087597150, 23511579564, 90659983064, 349090305487, 1342531370565, 5157512878694, 19794331541270, 75905591609120, 290857683782250, 1113774550930080

Offset

4,1

Links

Alois P. Heinz, Table of n, a(n) for n = 4..1716 (terms n = 4..59 from R. H. Hardin)

Maple

b:= proc(n, i, k) option remember; `if`(n=0, 1,
      `if`(i=0, 0, add(b(n-j, i-1, k), j=0..min(n, k))))
    end:
a:= n-> (k-> b(n$2, k)-b(n$2, k-1))(4):
seq(a(n), n=4..30);  # Alois P. Heinz, Aug 17 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_] := If[n == 0, 1, b[n, n, 4] - b[n, n, 3]];
Table[a[n], {n, 4, 30}] (* Jean-François Alcover, Aug 28 2022, after Maple program *)

Crossrefs

Column 4 of A180281.

Sequence in context: A027156 A017964 A017965 * A065180 A229245 A328153

Adjacent sequences: A180281 A180282 A180283 * A180285 A180286 A180287

Keyword

nonn

Author

R. H. Hardin, Aug 24 2010

Status

approved