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

1,2

Links

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

Formula

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A051914 A104519 A321684 * A118426 A082008 A105330

Adjacent sequences: A117217 A117218 A117219 * A117221 A117222 A117223

Keyword

nonn

Author

Reinhard Zumkeller, Mar 04 2006

Status

approved