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

0, 1, 5, 19, 54, 141, 331, 733, 1527, 3060, 5888, 11004, 19978, 35452, 61538, 104875, 175618, 289656, 470914, 755880, 1198693, 1880246, 2918919, 4488553, 6840398, 10337947, 15500575, 23070000, 34094908, 50055877, 73026093, 105902689, 152706404, 219004225

Offset: 1

Author

Clark Kimberling, Mar 13 2012

Keywords

• nonn

Examples

			The 5 partitions of 9 with parts <3 are as follows:
2+2+2+2+1
2+2+2+1+1+1
2+2+1+1+1+1+1
2+1+1+1+1+1+1+1
1+1+1+1+1+1+1+1+1.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A209818.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, 1,
      `if`(i<1, 0, b(n, i-1) +`if`(i>n, 0, b(n-i, i))))
    end:
a:= n-> b(3*n, n-1):
seq(a(n), n=1..50);  # Alois P. Heinz, Jul 09 2012

Mathematica

f[n_] := Length[Select[IntegerPartitions[3 n], First[#] <= n - 1 &]]; Table[f[n], {n, 1, 25}] (* 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 *)

Extensions

More terms from Alois P. Heinz, Jul 09 2012