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Number of partitions of 3-smooth numbers into parts not greater than 3.
7

%I #9 Jan 30 2020 06:40:44

%S 1,2,3,4,7,10,12,19,30,37,61,75,102,127,217,271,374,469,588,817,1027,

%T 1430,1801,2269,3169,3997,5043,5590,7057,8911,12481,15769,19927,22102,

%U 27937,35317,44652,49537,62641,79219,87894,111169,140617,177877,197377

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

%H Amiram Eldar, <a href="/A117220/b117220.txt">Table of n, a(n) for n = 1..10000</a>

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

%e 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.

%t 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 *)

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

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Mar 04 2006