A164111 Expansion of (1-x)/(1+4*x^2).

1, -1, -4, 4, 16, -16, -64, 64, 256, -256, -1024, 1024, 4096, -4096, -16384, 16384, 65536, -65536, -262144, 262144, 1048576, -1048576, -4194304, 4194304, 16777216, -16777216, -67108864, 67108864, 268435456, -268435456, -1073741824

Offset

0,3

Comments

Hankel transform of 1,1,0,2,0,6,0,70,... (which has g.f. 1+x/sqrt(1-4x^2). See A126869).

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = (-1)^C(n+1,2)*(4^(n/2)*(1+(-1)^n)/2 + 4^((n-1)/2)*(1-(-1)^n)/2).

a(n+3) = a(n+2)*a(n+1)/a(n). - Reinhard Zumkeller, Mar 04 2011

Mathematica

LinearRecurrence[{0, -4}, {1, -1}, 40] (* Harvey P. Dale, Sep 01 2015 *)
Rest[CoefficientList[Series[x*(1 - x)/(1 + 4*x^2), {x, 0, 50}], x]] (* G. C. Greubel, Sep 11 2017 *)

Prog

(PARI) x='x+O('x^50); Vec((1-x)/(1+4*x^2)) \\ G. C. Greubel, Sep 11 2017

Crossrefs

Sequence in context: A303072 A231839 A141125 * A056450 A164906 A213173

Adjacent sequences: A164108 A164109 A164110 * A164112 A164113 A164114

Keyword

easy,sign

Author

Paul Barry, Aug 10 2009

Status

approved