|
|
A271357
|
|
a(n) = k*Fibonacci(2*n+1) + (k+1)*Fibonacci(2*n), where k=3.
|
|
3
|
|
|
3, 10, 27, 71, 186, 487, 1275, 3338, 8739, 22879, 59898, 156815, 410547, 1074826, 2813931, 7366967, 19286970, 50493943, 132194859, 346090634, 906077043, 2372140495, 6210344442, 16258892831, 42566334051, 111440109322, 291753993915, 763821872423, 1999711623354
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (3+x) / (1-3*x+x^2).
a(n) = 3*a(n-1)-a(n-2) for n>1.
a(n) = (2^(-2-n)*((9-sqrt(5))*(3+sqrt(5))^(n+1) - (9+sqrt(5))*(3-sqrt(5))^(n+1))) / sqrt(5).
a(n) = 4*Fibonacci(2*n+2) - Fibonacci(2*n+1).
|
|
MATHEMATICA
|
Table[3Fibonacci[2n+1]+4Fibonacci[2n], {n, 0, 30}] (* or *) LinearRecurrence[ {3, -1}, {3, 10}, 30] (* Harvey P. Dale, Apr 05 2019 *)
|
|
PROG
|
(PARI) a(n) = 3*fibonacci(2*n+1) + 4*fibonacci(2*n)
(PARI) Vec((3+x)/(1-3*x+x^2) + O(x^50))
(Magma) k:=3; [k*Fibonacci(2*n+1)+(k+1)*Fibonacci(2*n): n in [0..30]]; // Bruno Berselli, Apr 06 2016
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
Changed offset and adapted definition, programs and formulas by Bruno Berselli, Apr 06 2016
|
|
STATUS
|
approved
|
|
|
|