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Number of terms in Zeckendorf representation of 9^n.
1

%I #12 Oct 19 2019 12:50:12

%S 1,2,3,5,6,7,8,11,12,12,13,18,16,15,19,18,20,20,23,21,23,28,28,33,25,

%T 33,37,38,35,31,41,46,38,50,45,49,49,44,45,52,50,52,58,58,53,54,54,55,

%U 67,57,65,67,66,74,77,80,76,79,76,72,74,83,79,77,88,83,78,87,76,88,87,94,97

%N Number of terms in Zeckendorf representation of 9^n.

%H Amiram Eldar, <a href="/A025501/b025501.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = A007895(A001019(n)). - _Michel Marcus_, May 09 2019

%e 9^2 = 81 = F(10) + F(8) + F(5) = 55 + 21 + 5. Hence a(2) = 3.

%e 9^3 = 729 = F(15) + F(11) + F(8) + F(6) + F(1) = 610 + 89 + 21 + 8 + 1. Hence a(3) = 5.

%t Table[Length[DeleteCases[NestWhileList[# - Fibonacci[Floor[Log[Sqrt[5] * # + 3/2]/Log[GoldenRatio]]] &, 9^n, # > 1 &], 0]], {n, 0, 80}] (* _Alonso del Arte_, May 09 2019 *)

%Y Cf. A001019, A007895.

%K nonn

%O 0,2

%A _Clark Kimberling_