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A320770 a(n) = (-1)^floor(n/4) * 2^floor(n/2). 1
1, 1, 2, 2, -4, -4, -8, -8, 16, 16, 32, 32, -64, -64, -128, -128, 256, 256, 512, 512, -1024, -1024, -2048, -2048, 4096, 4096, 8192, 8192, -16384, -16384, -32768, -32768, 65536, 65536, 131072, 131072, -262144, -262144, -524288, -524288, 1048576, 1048576 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

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

FORMULA

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

G.f.. A(x) = 1/(1 - x/(1 - x/(1 + 2*x/(1 - 4*x/(1 + 3*x/(1 + 5*x/(3 - 2*x))))))).

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

a(n) = c(n) * (-2)^n * a(-n) for all n in Z where c(4*k+2) = -1 else 1.

a(n) = a(n+1) = (1+I)^n * (-I)^(n/2) * (-1)^floor(n/4) if n = 2*k.

a(n) =  (-1)^floor(n/4) * A016116(n).

EXAMPLE

G.f. = 1 + x + 2*x^2 + 2*x^3 - 4*x^4 - 4*x^5 - 8*x^6 - 8*x^7 + ...

MATHEMATICA

a[ n_] := (-1)^Quotient[n, 4] * 2^Quotient[n, 2];

PROG

(PARI) {a(n) = (-1)^floor(n/4) * 2^floor(n/2)};

(MAGMA) [(-1)^Floor(n/4)* ^Floor(n/2): n in [0..50]]; // G. C. Greubel, Oct 27 2018

CROSSREFS

Cf. A016116.

Sequence in context: A117575 A131572 A152166 * A016116 A060546 A163403

Adjacent sequences:  A320767 A320768 A320769 * A320771 A320772 A320773

KEYWORD

sign

AUTHOR

Michael Somos, Oct 20 2018

STATUS

approved

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Last modified April 20 06:52 EDT 2021. Contains 343121 sequences. (Running on oeis4.)