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%I #65 Jul 07 2023 05:41:11
%S 1,0,0,1,0,1,1,0,2,1,1,1,0,2,2,1,2,1,1,1,0,3,2,2,2,1,2,2,1,2,1,1,1,0,
%T 3,3,2,3,2,2,2,1,3,2,2,2,1,2,2,1,2,1,1,1,0,4,3,3,3,2,3,3,2,3,2,2,2,1,
%U 3,3,2,3,2,2,2,1,3,2,2,2,1,2,2,1,2,1,1,1,0,4,4,3,4,3,3,3,2,4,3,3
%N Number of 0's in Stolarsky representation of n.
%C For the Stolarsky representation of n, see the C. Mongoven link.
%C a(n+1), n >= 1, gives the size of the n-th generation of each of the "[male-female] pair of Fibonacci rabbits" in the Fibonacci rabbits tree read right-to-left by row, the first pair (the root) being the 0th generation. (Cf. OEIS Wiki link below.) - _Daniel Forgues_, May 07 2015
%C From _Daniel Forgues_, May 07 2015: (Start)
%C Concatenation of:
%C 0: 1,
%C 1: 0,
%C 2: 0,
%C 3: 1, 0,
%C 4: 1, 1, 0,
%C 5: 2, 1, 1, 1, 0,
%C 6: 2, 2, 1, 2, 1, 1, 1, 0,
%C (...),
%C where row n, n >= 3, is row n-1 prepended by incremented row n-2. (End)
%C For n >= 3, this algorithm yields the next F_n terms of the sequence, where F_n is the n-th Fibonacci number (A000045). Since it is asymptotic to (phi^n)/sqrt(5), the number of terms thus obtained grows exponentially at each step! - _Daniel Forgues_, May 22 2015
%H Kenny Lau, <a href="/A200650/b200650.txt">Table of n, a(n) for n = 1..20000</a>
%H Casey Mongoven, <a href="/A200648/a200648.txt">Description of Stolarsky Representations</a>.
%H OEIS Wiki, <a href="/wiki/Fibonacci_rabbits_per_generation">Fibonacci rabbits per generation</a>.
%F a(n) = A200648(n) - A200649(n). - _Amiram Eldar_, Jul 07 2023
%e The Stolarsky representation of 19 is 11101. This has one 0. So a(19) = 1.
%t stol[n_] := stol[n] = If[n == 1, {}, If[n != Round[Round[n/GoldenRatio]*GoldenRatio], Join[stol[Floor[n/GoldenRatio^2] + 1], {0}], Join[stol[Round[n/GoldenRatio]], {1}]]];
%t a[n_] := If[n == 1, 1, Count[stol[n], 0]]; Array[a, 100] (* _Amiram Eldar_, Jul 07 2023 *)
%o (PARI) stol(n) = {my(phi=quadgen(5)); if(n==1, [], if(n != round(round(n/phi)*phi), concat(stol(floor(n/phi^2) + 1), [0]), concat(stol(round(n/phi)), [1])));}
%o a(n) = if(n == 1, 1, my(s = stol(n)); #s - vecsum(s)); \\ _Amiram Eldar_, Jul 07 2023
%Y Cf. A000045, A200648, A200649, A200651.
%K nonn,base,easy
%O 1,9
%A _Casey Mongoven_, Nov 19 2011
%E Corrected and extended by _Kenny Lau_, Jul 04 2016
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