A236191 a(n) = (-1)^floor( (n-1) / 3 ) * F(n), where F = Fibonacci.

0, 1, 1, 2, -3, -5, -8, 13, 21, 34, -55, -89, -144, 233, 377, 610, -987, -1597, -2584, 4181, 6765, 10946, -17711, -28657, -46368, 75025, 121393, 196418, -317811, -514229, -832040, 1346269, 2178309, 3524578, -5702887, -9227465, -14930352, 24157817, 39088169

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,-4,0,0,1).

Formula

G.f.: (x + x^2 + 2*x^3 + x^4 - x^5) / (1 + 4*x^3 - x^6).

a(n) = -4 * a(n-3) + a(n-6). a(-n) = (-1)^floor( (n-2) / 3) * a(n) for all n in Z.

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

Example

G.f. = x + x^2 + 2*x^3 - 3*x^4 - 5*x^5 - 8*x^6 + 13*x^7 + 21*x^8 + ...

Mathematica

a[ n_] := (-1)^Quotient[n-1, 3] Fibonacci[n];
CoefficientList[Series[(x + x^2 + 2 x^3 + x^4 - x^5)/(1 + 4 x^3 - x^6), {x, 0, 50}], x] (* Vincenzo Librandi, Jan 20 2014 *)

Prog

(PARI) {a(n) = (-1)^( (n-1) \ 3) * fibonacci( n)};
(Magma) I:=[0, 1, 1, 2, -3, -5]; [n le 6 select I[n] else -4*Self(n-3)+Self(n-6): n in [1..40]]; // Vincenzo Librandi, Jan 20 2014

Crossrefs

Cf. A000045.

Sequence in context: A132636 A152163 A039834 * A333378 A000045 A324969

Adjacent sequences: A236188 A236189 A236190 * A236192 A236193 A236194

Keyword

sign,easy

Author

Michael Somos, Jan 19 2014

Status

approved