|
Search: id:A153884
|
|
|
| A153884 |
|
a(n) = ((7+sqrt(5))^n-(7-sqrt(5))^n)/(2*sqrt(5)). |
|
+0
1
|
|
| 1, 14, 152, 1512, 14480, 136192, 1269568, 11781504, 109080064, 1008734720, 9322763264, 86134358016, 795679428608, 7349600247808, 67884508610560, 627000709644288, 5791091556155392, 53487250561826816, 494013479394738176
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Fifth binomial transform of A048878.
lim_{n -> infinity} a(n)/a(n-1) = 7+sqrt(5) = 9.236067977499789696....
|
|
FORMULA
|
a(n) = 14*a(n-1)-44*a(n-2) for n>1; a(0)=0, a(1)=1. G.f.: x/(1-14*x+44*x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 03 2009]
|
|
PROGRAM
|
(MAGMA) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-5); S:=[ ((7+r)^n-(7-r)^n)/(2*r): n in [1..19] ]; [ 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)), A048878.
Sequence in context: A153598 A037960 A016163 this_sequence A154239 A016215 A097227
Adjacent sequences: A153881 A153882 A153883 this_sequence A153885 A153886 A153887
|
|
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
|
|
|
Search completed in 0.002 seconds
|
