|
|
A162561
|
|
a(n) = ((4+sqrt(3))*(5+sqrt(3))^nv+v(4-sqrt(3))*(5-sqrt(3))^n)/2.
|
|
2
|
|
|
4, 23, 142, 914, 6016, 40052, 268168, 1800536, 12105664, 81444848, 548123872, 3689452064, 24835795456, 167190009152, 1125512591488, 7576945713536, 51008180122624, 343388995528448, 2311709992586752, 15562542024241664
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
Third binomial transform of A077236. Fourth binomial transform of A162559. Fifth binomial transform of A162766.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 10*a(n-1) - 22*a(n-2) for n > 2; a(0) = 4, a(1) = 23.
G.f.: (4-17*x)/(1-10*x+22*x^2).
|
|
MATHEMATICA
|
LinearRecurrence[{10, -22}, {4, 23}, 30] (* Harvey P. Dale, Mar 27 2013 *)
|
|
PROG
|
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-3); S:=[ ((4+r)*(5+r)^n+(4-r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 14 2009
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Al Hakanson (hawkuu(AT)gmail.com), Jul 06 2009
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|