|
| |
|
|
A153886
|
|
a(n) = ((9+sqrt(5))^n-(9-sqrt(5))^n)/(2*sqrt(5)).
|
|
0
| |
|
|
1, 18, 248, 3096, 36880, 428544, 4910912, 55827072, 631657984, 7126986240, 80279745536, 903384465408, 10159659716608, 114216655527936, 1283765661040640, 14427316078608384, 162125499175862272
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| lim_{n -> infinity} a(n)/a(n-1) = 9+sqrt(5) = 11.236067977499789696....
|
|
|
FORMULA
| a(n) = 18*a(n-1)-76*a(n-2) for n>1; a(0)=0, a(1)=1. G.f.: x/(1-18*x+76*x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr) and Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 03 2009]
|
|
|
MATHEMATICA
| Join[{a=1, b=18}, Table[c=18*b-76*a; a=b; b=c, {n, 40}]] (*From Vladimir Joseph Stephan Orlovsky, Feb 09 2011*)
LinearRecurrence[{18, -76}, {1, 18}, 20] (* From Harvey P. Dale, June 06 2011 *)
|
|
|
PROG
| (MAGMA) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-5); S:=[ ((9+r)^n-(9-r)^n)/(2*r): n in [1..17] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 04 2009]
|
|
|
CROSSREFS
| Cf. A002163 (decimal expansion of sqrt(5)).
Sequence in context: A153600 A016183 A016239 * A154241 A154250 A154350
Adjacent sequences: A153883 A153884 A153885 * A153887 A153888 A153889
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Al Hakanson (hawkuu(AT)gmail.com), Jan 03 2009
|
|
|
EXTENSIONS
| Extended beyond a(7) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 04 2009
Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 11 2009
|
| |
|
|
