|
|
A163069
|
|
a(n) = ((4+sqrt(5))*(1+sqrt(5))^n + (4-sqrt(5))*(1-sqrt(5))^n)/2.
|
|
3
|
|
|
4, 9, 34, 104, 344, 1104, 3584, 11584, 37504, 121344, 392704, 1270784, 4112384, 13307904, 43065344, 139362304, 450985984, 1459421184, 4722786304, 15283257344, 49457659904, 160048349184, 517927337984, 1676048072704
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 2*a(n-1) + 4*a(n-2) for n > 1; a(0) = 4, a(1) = 9.
G.f.: (4+x)/(1-2*x-4*x^2).
|
|
MATHEMATICA
|
LinearRecurrence[{2, 4}, {4, 9}, 30] (* G. C. Greubel, Jan 08 2018 *)
|
|
PROG
|
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-5); S:=[ ((4+r)*(1+r)^n+(4-r)*(1-r)^n)/2: n in [0..23] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 21 2009
(PARI) x='x+O('x^30); Vec((4+x)/(1-2*x-4*x^2)) \\ G. C. Greubel, Jan 08 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Al Hakanson (hawkuu(AT)gmail.com), Jul 20 2009
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|