A306637 a(n) = Fibonacci(n) * A128834(n).

0, 1, 1, 0, -3, -5, 0, 13, 21, 0, -55, -89, 0, 233, 377, 0, -987, -1597, 0, 4181, 6765, 0, -17711, -28657, 0, 75025, 121393, 0, -317811, -514229, 0, 1346269, 2178309, 0, -5702887, -9227465, 0, 24157817, 39088169, 0, -102334155, -165580141, 0, 433494437

Offset: 0

Author

Michael Somos, Mar 02 2019

Keywords

• sign
• easy

Comments

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.

Examples

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

Links

• Index entries for linear recurrences with constant coefficients, signature (1,-2,-1,-1).

Crossrefs

Cf. A000045, A128834.

Programs

Mathematica

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

PARI

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

Formula

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

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

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

a(n) = A275858(n-1)+A275858(n-3). - R. J. Mathar, Sep 24 2021