A166577 Inverse binomial transform of A166517.

1, 4, -5, 10, -20, 40, -80, 160, -320, 640, -1280, 2560, -5120, 10240, -20480, 40960, -81920, 163840, -327680, 655360, -1310720, 2621440, -5242880, 10485760, -20971520, 41943040, -83886080, 167772160, -335544320, 671088640, -1342177280, 2684354560, -5368709120

Offset

0,2

Comments

The definition assumes that the offset of A166517 is changed to 0.

A166517 mod 9 yields a periodic sequence with period 1, 5, 4, 8, 7, 2.

This set of numbers in the period appears also in A153130, A146501, and A166304.

Links

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

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

Formula

a(n) = -2*a(n-1), n>2.

a(n) = (-1)^(n+1)*A020714(n-2), n>1.

From Colin Barker, Jan 07 2013: (Start)

a(n) = -5*(-1)^n*2^(n-2) for n>1.

G.f.: (3*x^2+6*x+1)/(2*x+1). (End)

E.g.f.: (9/4) + (3/2)*x - (5/4)*exp(-2*x). - Alejandro J. Becerra Jr., Feb 15 2021

Mathematica

Join[{1, 4}, NestList[-2#&, -5, 40]] (* Harvey P. Dale, Aug 02 2012 *)
Join[{1, 4}, LinearRecurrence[{-2}, {-5}, 48]] (* G. C. Greubel, May 17 2016 *)

Crossrefs

Cf. A010716, A010692, A010859.

Sequence in context: A185875 A354080 A049898 * A242960 A288141 A203853

Adjacent sequences: A166574 A166575 A166576 * A166578 A166579 A166580

Keyword

sign,easy

Author

Paul Curtz, Oct 17 2009

Extensions

Edited, comments not concerning this sequence removed, and extended by R. J. Mathar, Oct 21 2009

Status

approved