A272665 Imaginary parts of b(n) sequence used to define A143056.

0, 0, 1, 2, 4, 6, 7, 4, -8, -36, -87, -162, -244, -278, -145, 360, 1520, 3608, 6641, 9882, 11028, 5166, -16073, -64084, -149528, -272076, -399911, -436682, -179684, 712530, 2698335, 6192720, 11140064, 16170928, 17258081, 6043314, -31395292, -113477674

Offset: 1

Author

N. J. A. Sloane, May 17 2016

Keywords

• sign
• easy

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (2,0,-2,-1).

Crossrefs

Cf. A143056.

Programs

Mathematica

Im[Fibonacci[Range[0, 20], 1 + I]] (* Vladimir Reshetnikov, Oct 04 2016 *)
LinearRecurrence[{2, 0, -2, -1}, {0, 0, 1, 2}, 36] (* Robert G. Wilson v, Oct 05 2016 *)

PARI

concat(vector(2), Vec(x^3/(1-2*x+2*x^3+x^4) + O(x^50))) \\ Colin Barker, May 17 2016

Formula

From Colin Barker, May 17 2016: (Start)

a(n) = 2*a(n-1)-2*a(n-3)-a(n-4) for n>4.

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

(End)

a(n) = (sin((n-1)*theta)*(tau^(n-1) + (-tau)^(1-n))*phi^(3/2) - cos((n-1)*theta)*(tau^(n-1) - (-tau)^(1-n))/phi^(3/2))/(2*sqrt(5)), where phi=(1+sqrt(5))/2, tau=sqrt(phi+sqrt(phi)), theta=arctan(phi^(-3/2)). - Vladimir Reshetnikov, Oct 04 2016