This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A140167 a(n) = (-1)*a(n-1) + 3*a(n-2). 4
 -1, 1, -4, 7, -19, 40, -97, 217, -508, 1159, -2683, 6160, -14209, 32689, -75316, 173383, -399331, 919480, -2117473, 4875913, -11228332, 25856071, -59541067, 137109280, -315732481, 727060321 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS A140165 is a companion sequence. LINKS Index to sequences with linear recurrences with constant coefficients, signature (-1,3). [From R. J. Mathar, Dec 12 2009] FORMULA a(n) = (-1)*a(n-1) + 3*a(n-2), given a(1) = -1, a(2) = 1. a(n) = term (1,2) of X^n, where X = the 2x2 matrix [1,-1; -1,-2]. a(n)=-(1/2)*[-1/2+(1/2)*sqrt(13)]^n-(1/2)*[-1/2-(1/2)*sqrt(13)]^n-(1/26)*sqrt(13)*[-1/2-(1/2) *sqrt(13)]^n+(1/26)*[-1/2+(1/2)*sqrt(13)]^n*sqrt(13), with n>=0 [From Paolo P. Lava, Aug 01 2008] a(n)=(-1)^n*A006130(n-1). G.f.: -x/(1+x-3*x^2). [From R. J. Mathar, Dec 12 2009] EXAMPLE a(5) = -19 = (-1)*7 + 3*(-4). a(5) = -19 = term (1,2) of X^5 since X^5 = [ -2, -19; -19, -59]. CROSSREFS Cf. A140165. Sequence in context: A006381 A102991 A062306 * A006130 A182228 A182646 Adjacent sequences:  A140164 A140165 A140166 * A140168 A140169 A140170 KEYWORD sign AUTHOR Gary W. Adamson, May 10 2008 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
Recent Additions | More pages | Superseeker | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified May 24 18:04 EDT 2013. Contains 225629 sequences.