A180283 - OEIS

%I #16 Aug 28 2022 04:17:57

%S 3,12,50,195,735,2716,9912,35850,128865,461175,1645215,5855941,

%T 20810153,73870748,262029364,929031504,3293120337,11672207262,

%U 41373395052,146674116501,520093043437,1844704839175,6544970763175,23229252652125

%N Number of arrangements of n indistinguishable balls in n boxes with the maximum number of balls in any box equal to 3.

%H 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 f:= proc(m,n) option remember;

%p   if m > 3*n or m < 3 then return 0 fi;

%p   g(m-3,n-1) + add(procname(m-i,n-1),i=0..2)

%p end proc:

%p g:= proc(m,n) option remember;

%p   if m > 3*n then return 0 fi;

%p   add(procname(m-i,n-1), i=0..min(m,3))

%p end proc:

%p g(0,0):= 1:

%p seq(f(n,n),n=3..30); # _Robert Israel_, May 03 2018

%t 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 a[n_] := b[n, n, 3] - b[n, n, 2];

%t Table[a[n], {n, 3, 30}] (* _Jean-François Alcover_, Aug 28 2022, after _Alois P. Heinz_ in A180281 *)

%Y Column 3 of A180281.

%K nonn

%O 3,1

%A _R. H. Hardin_, Aug 24 2010