A164305 a(n) = 6*a(n-1) - 7*a(n-2) for n > 1; a(0) = 3, a(1) = 17.

3, 17, 81, 367, 1635, 7241, 32001, 141319, 623907, 2754209, 12157905, 53667967, 236902467, 1045739033, 4616116929, 20376528343, 89946351555, 397042410929, 1752630004689, 7736483151631, 34150488876963, 150747551200361, 665431885063425, 2937358451978023

Offset

0,1

Comments

Binomial transform of A164304. Third binomial transform of A164654. Inverse binomial transform of A164535.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..169 from Vincenzo Librandi)

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) = 3, a(1) = 17.

G.f.: (3-x)/(1-6*x+7*x^2).

a(n) = ((3+4*sqrt(2))*(3+sqrt(2))^n + (3-4*sqrt(2))*(3-sqrt(2))^n)/2.

E.g.f.: (3*cosh(sqrt(2)*x) + 4*sqrt(2)*sinh(sqrt(2)*x))*exp(3*x). - G. C. Greubel, Sep 13 2017

Mathematica

LinearRecurrence[{6, -7}, {3, 17}, 30] (* Harvey P. Dale, Jun 03 2015 *)

Prog

(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((3+4*r)*(3+r)^n+(3-4*r)*(3-r)^n)/2: n in [0..21] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 20 2009
(PARI) x='x+O('x^50); Vec((3-x)/(1-6*x+7*x^2)) \\ G. C. Greubel, Sep 13 2017

Crossrefs

Cf. A164304, A164654, A164535.

Sequence in context: A062224 A217958 A093568 * A202247 A225342 A362390

Adjacent sequences: A164302 A164303 A164304 * A164306 A164307 A164308

Keyword

nonn,easy

Author

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

Extensions

Edited and extended beyond a(5) by Klaus Brockhaus, Aug 20 2009

Status

approved