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%I #12 Jan 24 2017 20:29:12
%S 1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,5,6,6,6,6,7,8,8,8,8,9,10,10,10,
%T 10,11,12,12,12,13,14,15,15,15,16,17,18,18,18,19,20,21,21,21,22,23,24,
%U 24,25,26,27,28,28,29,30,31,33,33,34,35,36,38,38
%N Number of partitions of n into parts of the form 3^k - 2^k, cf. A001047.
%H Reinhard Zumkeller, <a href="/A241766/b241766.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: Product_{k>=1} 1/(1 - x^(3^k-2^k)). - _Ilya Gutkovskiy_, Jan 23 2017
%e A001047(1..4) = {1, 5, 19, 65}:
%e a(18) = #{5+5+5+1+1+1, 5+5+8x1, 5+13x1, 18x1} = 4;
%e a(19) = #{19, 5+5+5+1+1+1+1, 5+5+9x1, 5+14x1, 19x1} = 5;
%e a(20) = #{19+1, 5+5+5+5, 5+5+5+5x1, 5+5+10x1, 5+15x1, 20x1} = 6;
%e a(21) = #{19+1+1, 5+5+5+5+1, 5+5+5+6x1, 5+5+11x1, 5+16x1, 21x1} = 6.
%t nmax = 100; CoefficientList[Series[Product[1/(1 - x^(3^k-2^k)), {k, 1, Floor[Log[nmax]/Log[2]] + 1}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jan 24 2017 *)
%o (Haskell)
%o a241766 = p $ tail a001047_list where
%o p _ 0 = 1
%o p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m
%Y Cf. A001047, A241759.
%K nonn
%O 0,6
%A _Reinhard Zumkeller_, Apr 28 2014
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