A306637 - OEIS

%I #12 Apr 19 2023 00:34:19

%S 0,1,1,0,-3,-5,0,13,21,0,-55,-89,0,233,377,0,-987,-1597,0,4181,6765,0,

%T -17711,-28657,0,75025,121393,0,-317811,-514229,0,1346269,2178309,0,

%U -5702887,-9227465,0,24157817,39088169,0,-102334155,-165580141,0,433494437

%N a(n) = Fibonacci(n) * A128834(n).

%C 0 = a(n)*(+a(n) +2*a(n+1) +2*a(n+2)) -a(n+3)*(2*a(n+1) -2*a(n+2) +a(n+3)) for all n in Z.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,-2,-1,-1).

%F G.f.: (x + x^3) / (1 - x + 2*x^2 + x^3 + x^4). a(3*n) = 0.

%F G.f.: 1 / (1-x / (1+x / (1-3*x / (1+4*x / (3+1*x / (2-3*x / (1+2*x))))))).

%F a(n) = (-1)^n * a(-n) = a(n-1) - 2*a(n-2) - a(n-3) - a(n-4) for all n in Z.

%F a(n) = A275858(n-1)+A275858(n-3). - _R. J. Mathar_, Sep 24 2021

%e G.f. = x + x^2 - 3*x^4 - 5*x^5 + 13*x^7 + 21*x^8 - 55*x^10 - 89*x^11 + ...

%t a[ n_] := Fibonacci[n] (-1)^Quotient[n, 3] Min[Mod[n, 3], 1];

%o (PARI) {a(n) = fibonacci(n) * (-1)^(n\3) * (n%3>0)};

%Y Cf. A000045, A128834.

%K sign,easy

%O 0,5

%A _Michael Somos_, Mar 02 2019