OFFSET
1,2
COMMENTS
Also, the number of partitions of 4n into n parts. - Seiichi Manyama, May 07 2018
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000
FORMULA
a(n) ~ exp(Pi*sqrt(2*n))/(12*sqrt(3)*n). - Vaclav Kotesovec, May 25 2015
EXAMPLE
The 4 partitions of 6 with parts <3:
2+2+2, 2+2+1+1, 2+1+1+1+1, 1+1+1+1+1+1.
From Seiichi Manyama, May 07 2018: (Start)
n | Partitions of 4n into n parts
--+-------------------------------------------
1 | 4;
2 | 7+1, 6+2, 5+3, 4+4;
3 | 10+1+1, 9+2+1, 8+3+1, 8+2+2, 7+4+1, 7+3+2,
| 6+5+1, 6+4+2, 6+3+3, 5+5+2, 5+4+3, 4+4+4; (End)
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):
seq(a(n), n=1..50); # Alois P. Heinz, Jul 09 2012
MATHEMATICA
f[n_] := Length[Select[IntegerPartitions[3n], First[#] <= n &]]; Table[f[n], {n, 1, 25}] (* A209818 *)
Table[SeriesCoefficient[Product[1/(1-x^k), {k, 1, n}], {x, 0, 3*n}], {n, 1, 20}] (* Vaclav Kotesovec, May 25 2015 *)
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]; Table[a[n], {n, 1, 50}] (* Jean-François Alcover, Oct 28 2015, after Alois P. Heinz *)
Table[Length@IntegerPartitions[4n, {n}], {n, 25}] (* Vladimir Reshetnikov, Jul 24 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Mar 13 2012
EXTENSIONS
More terms from Alois P. Heinz, Jul 09 2012
STATUS
approved