|
|
A056123
|
|
a(n) = 3*a(n-1) - a(n-2) with a(0)=1, a(1)=11.
|
|
1
|
|
|
1, 11, 32, 85, 223, 584, 1529, 4003, 10480, 27437, 71831, 188056, 492337, 1288955, 3374528, 8834629, 23129359, 60553448, 158530985, 415039507, 1086587536, 2844723101, 7447581767, 19498022200, 51046484833, 133641432299
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) = {11*[((3+sqrt(5))/2)^n - ((3-sqrt(5))/2)^n] - [((3+sqrt(5))/2)^(n-1) - ((3-sqrt(5))/2)^(n-1)]}/sqrt(5).
G.f.: (1+8*x)/(1-3*x+x^2).
a(n) = 6*Lucas(2n+1) - Fibonacci(2n+5).
a(n) = Fibonacci(2*n+2) + 8*Fibonacci(2*n).
E.g.f.: exp(3*t/2)*( cosh(sqrt(5)*t/2) + (19/sqrt(5))*sinh(sqrt(5)*t/2) ). (End)
|
|
MAPLE
|
with(combinat); seq( fiboacci(2*n+2) +8*fibonacci(2*n), n=0..30); # G. C. Greubel, Jan 17 2020
|
|
MATHEMATICA
|
Table[Fibonacci[2*n+2] +8*Fibonacci[2*n], {n, 0, 30}] (* G. C. Greubel, Jan 17 2020 *)
|
|
PROG
|
(PARI) vector(31, n, fibonacci(2*n) +8*fibonacci(2*n-2) ) \\ G. C. Greubel, Jan 17 2020
(Magma) [Fibonacci(2*n+2) +8*Fibonacci(2*n): n in [0..30]]; // G. C. Greubel, Jan 17 2020
(Sage) [fibonacci(2*n+2) +8*fibonacci(2*n) for n in (0..30)] # G. C. Greubel, Jan 17 2020
(GAP) List([0..30], n-> Fibonacci(2*n+2) +8*Fibonacci(2*n) ); # G. C. Greubel, Jan 17 2020
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|