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A123344 Expansion of (1+3*x)/(1+2*x). 3
1, 1, -2, 4, -8, 16, -32, 64, -128, 256, -512, 1024, -2048, 4096, -8192, 16384, -32768, 65536, -131072, 262144, -524288, 1048576, -2097152, 4194304, -8388608, 16777216, -33554432, 67108864, -134217728, 268435456, -536870912, 1073741824, -2147483648 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Inverse binomial transform of A000034.

Hankel transform is [1,-3,0,0,0,0,0,0,0,0,...].

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..200 from Vincenzo Librandi)

Index entries for linear recurrences with constant coefficients, signature (-2).

FORMULA

a(0)=1, a(n) = (-2)^(n-1) for n>0.

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

G.f.: 1/U(0)  where U(k)=  1 - x*(k+4) + x*(k+3)/U(k+1); (continued fraction, 1-step). - Sergei N. Gladkovskii, Oct 11 2012

E.g.f.: (3 - exp(-2*x))/2. - G. C. Greubel, Oct 12 2017

MAPLE

a:=n->mul(-2, k=0..n): seq(a(n), n=-2..30); # Zerinvary Lajos, Jan 22 2008

MATHEMATICA

Table[(-2)^(n - Sign[n]), {n, 0, 30}] (* Wesley Ivan Hurt, Feb 01 2014 *)

Join[{1}, LinearRecurrence[{-2}, {1}, 32]] (* Ray Chandler, Aug 12 2015 *)

PROG

(MAGMA) [1] cat [(-2)^(n-1): n in [1..35]]; // Vincenzo Librandi, Feb 14 2014

(PARI) x='x+O('x^50); Vec((1+3*x)/(1+2*x)) \\ G. C. Greubel, Oct 12 2017

CROSSREFS

Cf. A011782 (unsigned version).

Sequence in context: A034008 * A141531 A166444 A084633 A000079 A120617

Adjacent sequences:  A123341 A123342 A123343 * A123345 A123346 A123347

KEYWORD

easy,sign

AUTHOR

Philippe Deléham, Oct 11 2006

STATUS

approved

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Last modified October 22 03:52 EDT 2018. Contains 316431 sequences. (Running on oeis4.)