A117220 Number of partitions of 3-smooth numbers into parts not greater than 3.

1, 2, 3, 4, 7, 10, 12, 19, 30, 37, 61, 75, 102, 127, 217, 271, 374, 469, 588, 817, 1027, 1430, 1801, 2269, 3169, 3997, 5043, 5590, 7057, 8911, 12481, 15769, 19927, 22102, 27937, 35317, 44652, 49537, 62641, 79219, 87894, 111169, 140617, 177877, 197377

Offset: 1

Author

Reinhard Zumkeller, Mar 04 2006

Keywords

• nonn

Examples

			a(9) = #{3+3+3, 3+3+2+1, 3+3+1+1+1, 3+2+2+2, 3+2+2+1+1, 3+2+1*[4], 3+1*[6],2+2+2+2+1, 2+2+2+1+1+1, 2+2+1*[4], 2+1*[7], 1*[9]} = 12.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001399, A003586, A090184, A117221, A117222.

Programs

Mathematica

s = {}; m = 13; Do[n = 3^k; While[n <= 3^m, AppendTo[s, n]; n*=2], {k, 0, m}]; f[n_] := Round[(n + 3)^2/12]; f /@ Union[s] (* Amiram Eldar, Jan 30 2020 *)

Formula

a(n) = A001399(A003586(n)).