|
Search: id:A106732
|
|
|
| A106732 |
|
First entry of the vector (M^n)v, where M is the 2 X 2 matrix [[0,-3],[1,5]] and v is the column vector [0,1]. |
|
+0
1
|
|
| 0, -3, -15, -66, -285, -1227, -5280, -22719, -97755, -420618, -1809825, -7787271, -33506880, -144172587, -620342295, -2669193714, -11484941685, -49417127283, -212630811360, -914902674951, -3936620940675, -16938396678522, -72882120570585
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
Real Pisot roots (the eigenvalues of M): (5-sqrt(13))/2=0.697224,(5+sqrt(13))/2= 4.30278
|
|
FORMULA
|
a(n)=first entry of v[n], where v[n]=Mv[n-1], M is the 2 X 2 matrix [[0, -3], [1, 5]], and v[0] is the column vector [0,1]. G.f.=-3x/(1-5x+3x^2). a(n)=5a(n-1)-3a(n-2); a(0)=0, a(1)=-3.
|
|
MAPLE
|
a[0]:=0: a[1]:=-3: for n from 2 to 22 do a[n]:=5*a[n-1]-3*a[n-2] od: seq(a[n], n=0..22);
|
|
MATHEMATICA
|
M = {{0, -3}, {1, 5}} v[1] = {0, 1} v[n_] := v[n] = M.v[n - 1] a = Table[Abs[v[n][[1]]], {n, 1, 50}]
|
|
CROSSREFS
|
Sequence in context: A080948 A098102 A001447 this_sequence A052981 A086200 A122558
Adjacent sequences: A106729 A106730 A106731 this_sequence A106733 A106734 A106735
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 30 2005
|
|
EXTENSIONS
|
Edited by njas, Apr 30 2006
|
|
|
Search completed in 0.002 seconds
|
