|
|
A078020
|
|
Expansion of (1-x)/(1-x+2*x^2).
|
|
6
|
|
|
1, 0, -2, -2, 2, 6, 2, -10, -14, 6, 34, 22, -46, -90, 2, 182, 178, -186, -542, -170, 914, 1254, -574, -3082, -1934, 4230, 8098, -362, -16558, -15834, 17282, 48950, 14386, -83514, -112286, 54742, 279314, 169830, -388798, -728458, 49138, 1506054, 1407778, -1604330, -4419886, -1211226, 7628546
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Equals the INVERT transform of [1, -1, -1, 1, 1, -1, -1, 1, 1, ...], i.e., 1 followed by repeats of (-1, -1, 1, 1, ...). - Gary W. Adamson, Sep 16 2008
Pisano period lengths: 1, 1, 8, 1, 24, 8, 21, 2, 24, 24, 10, 8, 168, 21, 24, 2, 144, 24, 360, 24, ... - R. J. Mathar, Aug 10 2012
|
|
LINKS
|
|
|
FORMULA
|
|
|
MATHEMATICA
|
LinearRecurrence[{1, -2}, {1, 0}, 50] (* or *) CoefficientList[Series[(1 - x)/(1-x+2*x^2), {x, 0, 50}], x] (* G. C. Greubel, Jun 29 2019 *)
|
|
PROG
|
(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1-x)/(1-x+2*x^2) )); // G. C. Greubel, Jun 29 2019
(Sage) ((1-x)/(1-x+2*x^2)).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, Jun 29 2019
(GAP) a:=[1, 0];; for n in [2..50] do a[n]:=a[n-1]-2*a[n-2]; od; a; # G. C. Greubel, Jun 29 2019
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|