A168075 revision #16
|
|
A168075
|
|
Expansion of (1+27x^2-54x^3)/((1+3x)^2*(1-3x+9 x^2)).
|
|
3
|
|
|
1, -3, 36, -189, 567, -2430, 9477, -28431, 104976, -373977, 1121931, -3897234, 13286025, -39858075, 133923132, -444816117, 1334448351, -4390765542, 14334558093, -43003674279, 139471376040, -449795187729, 1349385563187, -4330586226042, 13839047287569
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 2*(-3)^n*n + 3^n*(sin(Pi*n/3)/sqrt(3) + cos(Pi*n/3)). - Ilya Gutkovskiy, Jul 10 2016
|
|
MATHEMATICA
|
LinearRecurrence[{-3, 0, -27, -81}, {1, -3, 36, -189}, 50] (* G. C. Greubel, Jul 09 2016 *)
CoefficientList[Series[(1 + 27 x^2 - 54 x^3) / ((1 + 3 x)^2 (1 - 3 x + 9 x^2)), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 10 2016 *)
|
|
PROG
|
(PARI) Vec((1+27*x^2-54*x^3)/((1+3*x)^2*(1-3*x+9*x^2))+ O(x^30)) \\ Michel Marcus, Dec 03 2014
(MAGMA) I:=[1, -3, 36, -189]; [n le 4 select I[n] else -3*Self(n-1)-27*Self(n-3)-81*Self(n-4): n in [1..30]]; // Vincenzo Librandi, Jul 10 2016
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,sign
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
editing
|
|
|
|