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

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

1,3

Links

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

Example

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.

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 *)

Crossrefs

Cf. A209818.

Sequence in context: A200764 A285987 A055365 * A281156 A060100 A053733

Adjacent sequences: A209814 A209815 A209816 * A209818 A209819 A209820

Keyword

nonn

Author

Clark Kimberling, Mar 13 2012

Extensions

More terms from Alois P. Heinz, Jul 09 2012

Status

approved