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A164299 a(n) = ((1+4*sqrt(2))*(3+sqrt(2))^n + (1-4*sqrt(2))*(3-sqrt(2))^n)/2. 3
1, 11, 59, 277, 1249, 5555, 24587, 108637, 479713, 2117819, 9348923, 41268805, 182170369, 804140579, 3549650891, 15668921293, 69165971521, 305313380075, 1347718479803, 5949117218293, 26260673951137, 115920223178771 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A164298. Third binomial transform of A164587. Inverse binomial transform of A164300.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-7).

FORMULA

a(n) = 6*a(n-1) - 7*a(n-2) for n > 1; a(0) = 1, a(1) = 11.

G.f.: (1+5*x)/(1-6*x+7*x^2).

E.g.f.: (cosh(sqrt(2)*x) + 4*sqrt(2)*sinh(sqrt(2)*x))*exp(3*x). - G. C. Greubel, Sep 12 2017

MATHEMATICA

LinearRecurrence[{6, -7}, {1, 11}, 50] (* or *) CoefficientList[Series[(1 + 5*x)/(1 - 6*x + 7*x^2), {x, 0, 50}], x] (* G. C. Greubel, Sep 12 2017 *)

PROG

(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+4*r)*(3+r)^n+(1-4*r)*(3-r)^n)/2: n in [0..21] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 17 2009

(PARI) x='x+O('x^50); Vec((1+5*x)/(1-6*x+7*x^2)) \\ G. C. Greubel, Sep 12 2017

CROSSREFS

Cf. A164298, A164587, A164300.

Sequence in context: A217114 A249891 A186256 * A253207 A241860 A082884

Adjacent sequences:  A164296 A164297 A164298 * A164300 A164301 A164302

KEYWORD

nonn

AUTHOR

Al Hakanson (hawkuu(AT)gmail.com), Aug 12 2009

EXTENSIONS

Edited and extended beyond a(5) by Klaus Brockhaus, Aug 17 2009

STATUS

approved

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Last modified July 9 04:51 EDT 2020. Contains 335538 sequences. (Running on oeis4.)