|
|
A199853
|
|
Expansion of (1-3*x+x^3)/(1-2*x-x^2+x^3).
|
|
2
|
|
|
1, -1, -1, -3, -6, -14, -31, -70, -157, -353, -793, -1782, -4004, -8997, -20216, -45425, -102069, -229347, -515338, -1157954, -2601899, -5846414, -13136773, -29518061, -66326481, -149034250, -334876920, -752461609, -1690765888, -3799116465, -8536537209
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 2*a(n-1) + a(n-2) - a(n-3) with a(0)=1, a(1)=-1, a(2)=-1, a(3)=-3.
|
|
MATHEMATICA
|
RecurrenceTable[{a[1]==-1, a[2]== -1, a[3]== -3, a[n]== 2*a[n-1] + a[n-2] - a[n-3]}, a, {n, 30}] (* G. C. Greubel, Aug 13 2015 *)
CoefficientList[Series[(1-3x+x^3)/(1-2x-x^2+x^3), {x, 0, 30}], x] (* or *) LinearRecurrence[{2, 1, -1}, {1, -1, -1, -3}, 40] (* Harvey P. Dale, May 31 2021 *)
|
|
PROG
|
(PARI) Vec((1-3*x+x^3)/(1-2*x-x^2+x^3) + O(x^40)) \\ Michel Marcus, Aug 13 2015
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|