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

Author

Paul Curtz, Oct 17 2009

Keywords

• sign
• easy

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).

Crossrefs

Cf. A010716, A010692, A010859.

Programs

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 *)

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

Extensions

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