|
| |
|
|
A164602
|
|
a(n) = ((1+4*sqrt(2))*(1+2*sqrt(2))^n + (1-4*sqrt(2))*(1-2*sqrt(2))^n)/2.
|
|
3
|
|
|
|
1, 17, 41, 201, 689, 2785, 10393, 40281, 153313, 588593, 2250377, 8620905, 32994449, 126335233, 483631609, 1851609849, 7088640961, 27138550865, 103897588457, 397765032969, 1522813185137, 5829981601057, 22319655498073
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
Binomial transform of A164703. Inverse binomial transform of A164603.
|
|
|
LINKS
|
G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..177 from Vincenzo Librandi)
Index entries for linear recurrences with constant coefficients, signature (2,7).
|
|
|
FORMULA
|
a(n) = 2*a(n-1) + 7*a(n-2) for n > 1; a(0) = 1, a(1) = 17.
G.f.: (1+15*x)/(1-2*x-7*x^2).
E.g.f.: exp(x)*(cosh(2*sqrt(2)*x) + 4*sqrt(2)*sinh(2*sqrt(2)*x)). - G. C. Greubel, Aug 11 2017
|
|
|
MATHEMATICA
|
Simplify/@Table[1/2((1-4Sqrt[2])(1-2Sqrt[2])^n+(1+2Sqrt[2])^n(1+4 Sqrt[2])), {n, 0, 25}] (* Harvey P. Dale, Jul 26 2011 *)
|
|
|
PROG
|
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+4*r)*(1+2*r)^n+(1-4*r)*(1-2*r)^n)/2: n in [0..22] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 23 2009
(PARI) x='x+O('x^50); Vec((1+15*x)/(1-2*x-7*x^2)) \\ G. C. Greubel, Aug 11 2017
|
|
|
CROSSREFS
|
Cf. A164703, A164603.
Sequence in context: A201705 A165668 A269425 * A078847 A201028 A328022
Adjacent sequences: A164599 A164600 A164601 * A164603 A164604 A164605
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Al Hakanson (hawkuu(AT)gmail.com), Aug 17 2009
|
|
|
EXTENSIONS
|
Edited and extended beyond a(5) by Klaus Brockhaus, Aug 23 2009
|
|
|
STATUS
|
approved
|
| |
|
|
