|
| |
|
|
A156573
|
|
a(n) = 34*a(n-1)-a(n-2)-4232 for n > 2; a(1)=529, a(2)=13225.
|
|
3
| |
|
|
529, 13225, 444889, 15108769, 513249025, 17435353849, 592288777609, 20120383080625, 683500735959409, 23218904639535049, 788759257008228025, 26794595833640213569, 910227499086759029089, 30920940373116166771225
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| lim_{n -> infinity} a(n)/a(n-1) = 17+12*sqrt(2).
|
|
|
LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (35,-35,1).
|
|
|
FORMULA
| a(n) = 529*(2+(3-2*sqrt(2))*(17+12*sqrt(2))^n+(3+2*sqrt(2))*(17-12*sqrt(2))^n)/8.
G.f.: 529*x*(1-10*x+x^2)/((1-x)*(1-34*x+x^2)).
|
|
|
EXAMPLE
| a(3) = 34*a(2)-a(1)-4232 = 34*13225-529-4232 = 444889.
|
|
|
PROG
| (PARI) {m=14; v=concat([529, 13225], vector(m-2)); for(n=3, m, v[n]=34*v[n-1]-v[n-2]-4232); v}
|
|
|
CROSSREFS
| Second trisection of A156572. Equals 529*A008844.
Cf. A156164 (decimal expansion of 17+12*sqrt(2)), A156574, A156575.
Sequence in context: A067475 A052074 A112079 * A034987 A206861 A206955
Adjacent sequences: A156570 A156571 A156572 * A156574 A156575 A156576
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Feb 11 2009
|
|
|
EXTENSIONS
| Revised by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Feb 16 2009
G.f. corrected by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Sep 22 2009
|
| |
|
|
