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%I #17 Sep 08 2022 08:45:24
%S 0,1,2,5,8,21,34,89,144,377,610,1597,2584,6765,10946,28657,46368,
%T 121393,196418,514229,832040,2178309,3524578,9227465,14930352,
%U 39088169,63245986,165580141,267914296,701408733
%N a(2n) = A014445(n), a(2n+1) = A015448(n+1).
%H G. C. Greubel, <a href="/A117647/b117647.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,4,0,1).
%F a(n) = A059973(n+2) - A059973(n+1).
%F G.f.: x*(x+1)^2/(1 -4*x^2 -x^4).
%F a(n) = Fibonacci((6*n + 1 - (-1)^n)/4) = Fibonacci(A007494(n)). - _G. C. Greubel_, Jul 12 2021
%t Table[Fibonacci[(6*n+1 -(-1)^n)/4], {n, 0, 40}] (* _G. C. Greubel_, Jul 12 2021 *)
%o (Magma) I:=[0,1,2,5]; [n le 4 select I[n] else 4*Self(n-2) +Self(n-4): n in [1..41]]; // _G. C. Greubel_, Jul 12 2021
%o (Sage) [fibonacci((6*n+1-(-1)^n)/4) for n in [0..40]] # _G. C. Greubel_, Jul 12 2021
%Y Cf. A000045, A007494, A014445, A015448, A033887, A059973.
%K easy,nonn
%O 0,3
%A _Creighton Dement_, Apr 10 2006
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