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A270741 a(n) = (Fibonacci(n+2)-1) mod Fibonacci(floor(n/2)).

%I A270741 #14 Mar 29 2016 23:42:53
%S A270741 0,0,0,0,0,1,0,1,3,2,0,1,11,10,0,1,32,31,0,1,87,86,0,1,231,230,0,1,
%T A270741 608,607,0,1,1595,1594,0,1,4179,4178,0,1,10944,10943,0,1,28655,28654,
%U A270741 0,1,75023,75022,0,1,196416,196415,0,1,514227,514226,0,1,1346267,1346266,0,1,3524576,3524575,0,1
%N A270741 a(n) = (Fibonacci(n+2)-1) mod Fibonacci(floor(n/2)).
%C A270741 It appears that a(n)=1 gives same terms as A222945. - _Michel Marcus_, Mar 23 2016
%F A270741 Empirical g.f.: x^7*(1-x+2*x^2+x^3-3*x^4+3*x^5-6*x^6+5*x^7+x^8-x^9+2*x^10-2*x^11) / ((1-x)*(1+x^2)*(1+x^2-x^4)*(1-x^2-x^4)). - _Colin Barker_, Mar 23 2016
%e A270741 a(10) = 3 since (1 + 1 + 2 + 3 + 5 + 8 + 13 + 21 + 34 + 55) mod 5 = 143 mod 5 = 3.
%e A270741 a(11) = 2 since (1 + 1 + 2 + 3 + 5 + 8 + 13 + 21 + 34 + 55 + 89) mod 5 = 2.
%e A270741 a(12) = 0 since (1 + 1 + 2 + 3 + 5 + 8 + 13 + 21 + 34 + 55 + 89 + 144) mod 8 = 0.
%t A270741 Table[Mod[Fibonacci[n + 2] - 1, Fibonacci[Floor[n/2]]], {n, 2, 69}] (* _Michael De Vlieger_, Mar 23 2016 *)
%o A270741 (PARI) for(n=2, 1e2, print1((fibonacci(n+2)-1) % fibonacci(n\2), ", "));
%Y A270741 Cf. A000045, A000071, A270708.
%K A270741 nonn
%O A270741 2,9
%A A270741 _Altug Alkan_, Mar 22 2016