|
Search: id:A140167
|
|
|
| A140167 |
|
a(n) = (-1)*a(n-1) + 3*a(n-2). |
|
+0
3
|
|
| -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; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
A140165 is a companion sequence.
|
|
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 (ppl(AT)spl.at), Aug 01 2008]
|
|
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 this_sequence A006130 A133264 A127415
Adjacent sequences: A140164 A140165 A140166 this_sequence A140168 A140169 A140170
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
Gary W. Adamson (qntmpkt(AT)yahoo.com), May 10 2008
|
|
|
Search completed in 0.002 seconds
|
