cp's OEIS Frontend

A209817 Number of partitions of 3n in which every part is

%I A209817 #14 Oct 28 2015 13:21:37
%S A209817 0,1,5,19,54,141,331,733,1527,3060,5888,11004,19978,35452,61538,
%T A209817 104875,175618,289656,470914,755880,1198693,1880246,2918919,4488553,
%U A209817 6840398,10337947,15500575,23070000,34094908,50055877,73026093,105902689,152706404,219004225
%N A209817 Number of partitions of 3n in which every part is <n.
%H A209817 Alois P. Heinz, <a href="/A209817/b209817.txt">Table of n, a(n) for n = 1..1000</a>
%e A209817 The 5 partitions of 9 with parts <3 are as follows:
%e A209817 2+2+2+2+1
%e A209817 2+2+2+1+1+1
%e A209817 2+2+1+1+1+1+1
%e A209817 2+1+1+1+1+1+1+1
%e A209817 1+1+1+1+1+1+1+1+1.
%p A209817 b:= proc(n, i) option remember; `if`(n=0, 1,
%p A209817       `if`(i<1, 0, b(n, i-1) +`if`(i>n, 0, b(n-i, i))))
%p A209817     end:
%p A209817 a:= n-> b(3*n, n-1):
%p A209817 seq(a(n), n=1..50);  # _Alois P. Heinz_, Jul 09 2012
%t A209817 f[n_] := Length[Select[IntegerPartitions[3 n], First[#] <= n - 1 &]]; Table[f[n], {n, 1, 25}] (* A209817 *)
%t A209817 b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, b[n, i-1] + If[i>n, 0, b[n-i, i]]]]; a[n_] := b[3*n, n-1]; Table[a[n], {n, 1, 50}] (* _Jean-François Alcover_, Oct 28 2015, after _Alois P. Heinz_ *)
%Y A209817 Cf. A209818.
%K A209817 nonn
%O A209817 1,3
%A A209817 _Clark Kimberling_, Mar 13 2012
%E A209817 More terms from _Alois P. Heinz_, Jul 09 2012