|
| |
|
|
A156569
|
|
a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1)=37, a(2)=205.
|
|
3
| |
|
|
37, 205, 1193, 6953, 40525, 236197, 1376657, 8023745, 46765813, 272571133, 1588660985, 9259394777, 53967707677, 314546851285, 1833313400033, 10685333548913, 62278687893445, 362986793811757, 2115642074977097
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| lim_{n -> infinity} a(n)/a(n-1) = 3+2*sqrt(2).
|
|
|
LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (6,-1).
|
|
|
FORMULA
| a(n) = ((34+7*sqrt(2))*(3-2*sqrt(2))^n+(34-7*sqrt(2))*(3+2*sqrt(2))^n)/4.
G.f.: x*(37-17*x)/(1-6*x+x^2).
|
|
|
PROG
| (PARI) {m=19; v=concat([37, 205], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-v[n-2]); v}
|
|
|
CROSSREFS
| Third trisection of A156567.
Cf. A156035 (decimal expansion of 3+2*sqrt(2)), A156568, A156570.
Sequence in context: A109320 A053872 A141954 * A141984 A052166 A142010
Adjacent sequences: A156566 A156567 A156568 * A156570 A156571 A156572
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Feb 11 2009, Feb 16 2009
|
|
|
EXTENSIONS
| G.f. corrected by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Sep 22 2009
|
| |
|
|
