login
A180284
Number of arrangements of n indistinguishable balls in n boxes with the maximum number of balls in any box equal to 4.
1
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Aug 24 2010
STATUS
approved