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A272665
Imaginary parts of b(n) sequence used to define A143056.
3
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
1,4
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
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 *)
PROG
(PARI) concat(vector(2), Vec(x^3/(1-2*x+2*x^3+x^4) + O(x^50))) \\ Colin Barker, May 17 2016
CROSSREFS
Cf. A143056.
Sequence in context: A072646 A091476 A257578 * A114431 A167689 A058184
KEYWORD
sign,easy
AUTHOR
N. J. A. Sloane, May 17 2016
STATUS
approved