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%I #31 Jun 16 2019 16:14:58
%S 1,1,1,2,2,2,4,4,4,8,8,8,16,16,16,32,32,32,64,64,64,128,128,128,256,
%T 256,256,512,512,512,1024,1024,1024,2048,2048,2048,4096,4096,4096,
%U 8192,8192,8192,16384,16384,16384,32768,32768,32768,65536,65536,65536,131072,131072
%N a(n) = A158772(n-1)/21.
%C Triplicated A000079. Powers of 2 repeated 3 times.
%C a(n) is the number of ways of partitioning the set of the first n distinct positive Fibonacci numbers into two subsets whose sums differ at most by 1. a(6) = 2: 1,2,5,8/3,13; 1,2,13/3,5,8. - _Alois P. Heinz_, Jun 16 2019
%H G. C. Greubel, <a href="/A173862/b173862.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,2)
%F G.f. x*(1 + x + x^2)/(1 - 2*x^3). - _R. J. Mathar_, Nov 28 2011
%t Flatten[Table[c=2^n;{c,c,c},{n,0,20}]] (* _Harvey P. Dale_, Jul 20 2012 *)
%t CoefficientList[Series[x*(1 + x + x^2)/(1 - 2*x^3), {x,0,50}], x] (* _G. C. Greubel_, Apr 30 2017 *)
%o (PARI) a(n)=2^((n-1)\3) \\ _Charles R Greathouse IV_, Oct 03 2016
%Y Cf. A000045, A000079, A016116, A200672.
%K nonn,easy
%O 1,4
%A _Paul Curtz_, Nov 26 2010
%E More terms from _Harvey P. Dale_, Jul 20 2012