|
| |
|
|
A156156
|
|
a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1) = 13, a(2) = 53.
|
|
4
| |
|
|
13, 53, 305, 1777, 10357, 60365, 351833, 2050633, 11951965, 69661157, 406014977, 2366428705, 13792557253, 80388914813, 468540931625, 2730856674937, 15916599117997, 92768738033045, 540695829080273, 3151406236448593
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| lim_{n -> infinity} a(n)/a(n-1) = 3+2*sqrt(2).
|
|
|
FORMULA
| a(n) = ((50+31*sqrt(2))*(3-2*sqrt(2))^n+(50-31*sqrt(2))*(3+2*sqrt(2))^n)/4.
G.f.: x*(13-25*x)/(1-6*x+x^2).
|
|
|
PROG
| (PARI) {m=20; v=concat([13, 53], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-v[n-2]); v}
|
|
|
CROSSREFS
| First trisection of A155923.
Cf. A156035 (decimal expansion of 3+2*sqrt(2)), A156157, A156158.
Sequence in context: A139974 A142188 A206444 * A201486 A176617 A195024
Adjacent sequences: A156153 A156154 A156155 * A156157 A156158 A156159
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Feb 09 2009
|
|
|
EXTENSIONS
| Replaced abbreviation by sqrt(2) Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Feb 12 2009
G.f. corrected by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Sep 23 2009
|
| |
|
|
