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A180283
Number of arrangements of n indistinguishable balls in n boxes with the maximum number of balls in any box equal to 3.
1
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Aug 24 2010
STATUS
approved