|
|
A102345
|
|
a(n) = 3^n + (-1)^n.
|
|
6
|
|
|
2, 2, 10, 26, 82, 242, 730, 2186, 6562, 19682, 59050, 177146, 531442, 1594322, 4782970, 14348906, 43046722, 129140162, 387420490, 1162261466, 3486784402, 10460353202, 31381059610, 94143178826, 282429536482, 847288609442
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 2*a(n-1) + 3*a(n-2).
G.f.: 2*(1-x)/((1+x)*(1-3*x)).
E.g.f.: exp(-x) + exp(3*x).
|
|
MATHEMATICA
|
Table[3^n+(-1)^n, {n, 0, 30}] (* or *) LinearRecurrence[{2, 3}, {2, 2}, 30] (* Harvey P. Dale, Jun 19 2016 *)
|
|
PROG
|
(Sage) [lucas_number2(n, 2, -3) for n in range(0, 26)] # Zerinvary Lajos, Apr 30 2009
|
|
CROSSREFS
|
Apart from leading term, same as A084182.
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|