%I #14 Mar 29 2016 23:42:53

%S 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 608,607,0,1,1595,1594,0,1,4179,4178,0,1,10944,10943,0,1,28655,28654,

%U 0,1,75023,75022,0,1,196416,196415,0,1,514227,514226,0,1,1346267,1346266,0,1,3524576,3524575,0,1

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

%C It appears that a(n)=1 gives same terms as A222945. - _Michel Marcus_, Mar 23 2016

%F 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 a(10) = 3 since (1 + 1 + 2 + 3 + 5 + 8 + 13 + 21 + 34 + 55) mod 5 = 143 mod 5 = 3.

%e a(11) = 2 since (1 + 1 + 2 + 3 + 5 + 8 + 13 + 21 + 34 + 55 + 89) mod 5 = 2.

%e a(12) = 0 since (1 + 1 + 2 + 3 + 5 + 8 + 13 + 21 + 34 + 55 + 89 + 144) mod 8 = 0.

%t Table[Mod[Fibonacci[n + 2] - 1, Fibonacci[Floor[n/2]]], {n, 2, 69}] (* _Michael De Vlieger_, Mar 23 2016 *)

%o (PARI) for(n=2, 1e2, print1((fibonacci(n+2)-1) % fibonacci(n\2), ", "));

%Y Cf. A000045, A000071, A270708.

%K nonn

%O 2,9

%A _Altug Alkan_, Mar 22 2016