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%I #20 Apr 04 2020 10:22:00
%S 1,1,1,2,2,2,2,3,2,2,3,3,3,3,4,3,3,3,4,3,3,5,4,4,4,5,3,3,4,4,4,4,6,5,
%T 5,5,6,4,4,6,5,5,5,6,4,4,4,5,4,4,7,6,6,6,8,5,5,7,6,6,6,8,6,6,6,7,5,5,
%U 8,6,6,6,7,4,4,5,5,5,5,8,7,7,7,9,6,6,9,8,8,8,10,7,7,7,8,6,6,10,8,8,8,10,6,6,8
%N Number of partitions of n into distinct Lucas parts (A000032).
%H Alois P. Heinz, <a href="/A067595/b067595.txt">Table of n, a(n) for n = 0..15127</a>
%F G.f.: B(x) * (1 + x^2) where B(x) is the g.f. of A003263. [_Joerg Arndt_, Jul 14 2013]
%t n1 = 10; n2 = LucasL[n1]; (1 + x^2)*Product[1 + x^LucasL[n], {n, 1, n1}] + O[x]^n2 // CoefficientList[#, x]& (* _Jean-François Alcover_, Feb 17 2017, after _Joerg Arndt_ *)
%o (PARI)
%o L(n) = fibonacci(n+1) + fibonacci(n-1);
%o N = 66; x = 'x + O('x^N);
%o gf = prod(n=0, 11, 1 + x^L(n) );
%o \\gf = prod(n=1, 11, 1 + x^L(n) ) * (1+x^2); \\ same g.f.
%o Vec(gf) \\ _Joerg Arndt_, Jul 14 2013
%Y Cf. A000032, A000119.
%K easy,nonn,look
%O 0,4
%A _Naohiro Nomoto_, Jan 31 2002
%E Corrected a(0), _Joerg Arndt_, Jul 14 2013
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