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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.

%I A180283 #16 Aug 28 2022 04:17:57
%S A180283 3,12,50,195,735,2716,9912,35850,128865,461175,1645215,5855941,
%T A180283 20810153,73870748,262029364,929031504,3293120337,11672207262,
%U A180283 41373395052,146674116501,520093043437,1844704839175,6544970763175,23229252652125
%N A180283 Number of arrangements of n indistinguishable balls in n boxes with the maximum number of balls in any box equal to 3.
%H A180283 Robert Israel, <a href="/A180283/b180283.txt">Table of n, a(n) for n = 3..1795</a> (n=3..59 from R. H. Hardin)
%p A180283 f:= proc(m,n) option remember;
%p A180283   if m > 3*n or m < 3 then return 0 fi;
%p A180283   g(m-3,n-1) + add(procname(m-i,n-1),i=0..2)
%p A180283 end proc:
%p A180283 g:= proc(m,n) option remember;
%p A180283   if m > 3*n then return 0 fi;
%p A180283   add(procname(m-i,n-1), i=0..min(m,3))
%p A180283 end proc:
%p A180283 g(0,0):= 1:
%p A180283 seq(f(n,n),n=3..30); # _Robert Israel_, May 03 2018
%t A180283 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]}]]];
%t A180283 a[n_] := b[n, n, 3] - b[n, n, 2];
%t A180283 Table[a[n], {n, 3, 30}] (* _Jean-François Alcover_, Aug 28 2022, after _Alois P. Heinz_ in A180281 *)
%Y A180283 Column 3 of A180281.
%K A180283 nonn
%O A180283 3,1
%A A180283 _R. H. Hardin_, Aug 24 2010