|
|
A305650
|
|
a(n) = -1/3 * (u^n-1)*(v^n-1) with u = 1+sqrt(3), v = 1-sqrt(3).
|
|
1
|
|
|
1, 1, 9, 13, 61, 117, 421, 949, 2997, 7381, 21781, 56277, 160213, 424789, 1186389, 3189589, 8817493, 23883093, 65663317, 178568533, 489512277, 1334064469, 3651347797, 9962435925, 27244344661, 74380006741, 203315811669, 555257419093, 1517414896981, 4144807761237
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
LINKS
|
|
|
FORMULA
|
a(n) = a(n-1) + 6*a(n-2) - 2*a(n-3) - 4*a(n-4) for n > 4.
G.f.: x*(1 + 2*x^2) / ((1 - x)*(1 + 2*x)*(1 - 2*x - 2*x^2)). - Colin Barker, Jun 07 2018
|
|
MATHEMATICA
|
LinearRecurrence[{1, 6, -2, -4}, {1, 1, 9, 13}, 30] (* Harvey P. Dale, Jun 02 2019 *)
|
|
PROG
|
(PARI) Vec(x*(1 + 2*x^2) / ((1 - x)*(1 + 2*x)*(1 - 2*x - 2*x^2)) + O(x^40)) \\ Colin Barker, Jun 07 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|