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A294204 Number of partitions of n into distinct Lucas parts (A000032) greater than 1. 2

%I #6 Oct 25 2017 08:27:41

%S 1,0,1,1,1,1,1,2,0,2,1,2,1,2,2,1,2,1,3,0,3,2,2,2,2,3,0,3,1,3,1,3,3,2,

%T 3,2,4,0,4,2,3,2,3,3,1,3,1,4,0,4,3,3,3,3,5,0,5,2,4,2,4,4,2,4,2,5,0,5,

%U 3,3,3,3,4,0,4,1,4,1,4,4,3,4,3,6,0,6,3,5,3,5,5,2,5,2,6,0,6,4,4,4,4

%N Number of partitions of n into distinct Lucas parts (A000032) greater than 1.

%C Convolution of the sequences A067595 and A033999.

%H Ilya Gutkovskiy, <a href="/A294204/a294204.jpg">Extended graphical example</a>

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F G.f.: (1 + x^2)*Product_{k>=2} (1 + x^Lucas(k)).

%e a(9) = 2 because we have [7, 2] and [4, 3, 2].

%t CoefficientList[Series[(1 + x^2) Product[1 + x^LucasL[k], {k, 2, 15}], {x, 0, 100}], x]

%Y Cf. A000032, A033999, A067593, A067595, A239002, A294203.

%K nonn

%O 0,8

%A _Ilya Gutkovskiy_, Oct 24 2017

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