A100525 Bisection of A048654.

4, 22, 128, 746, 4348, 25342, 147704, 860882, 5017588, 29244646, 170450288, 993457082, 5790292204, 33748296142, 196699484648, 1146448611746, 6681992185828, 38945504503222, 226991034833504, 1323000704497802, 7711013192153308, 44943078448422046

Offset

0,1

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (6,-1).

Formula

G.f.: 2*(2-x)/(1-6*x+x^2). - Philippe Deléham, Nov 17 2008

a(0)=4, a(1)=22, a(n) = 6*a(n-1) - a(n-2) for n>1. - Philippe Deléham, Sep 19 2009

a(n) = 2*A038725(n+1). - R. J. Mathar, Sep 27 2014

a(n) = ( (5 + 4*sqrt(2))*(3 + 2*sqrt(2))^n - (5 - 4*sqrt(2))*(3 - 2*sqrt(2))^n )/(2*sqrt(2)). - Colin Barker, Oct 13 2015

From G. C. Greubel, Jun 28 2022: (Start)

a(n) = 2*( 2*ChebyshevU(n, 3) - ChenyshevU(n-1, 3) ).

E.g.f.: 2*exp(3*x)*( 2*cosh(2*sqrt(2)*x) + (5/(2*sqrt(2)))*sinh(2*sqrt(2)*x) ). (End)

Mathematica

CoefficientList[Series[(4-2x)/(1-6x+x^2), {x, 0, 33}], x] (* Vincenzo Librandi, Oct 13 2015 *)
LinearRecurrence[{6, -1}, {4, 22}, 30] (* Harvey P. Dale, Mar 25 2016 *)

Prog

(PARI) Vec((4-2*x)/(1-6*x+x^2) + O(x^40)) \\ Colin Barker, Oct 13 2015
(Magma) I:=[4, 22, 128]; [n le 3 select I[n] else 6*Self(n-1)-Self(n-2): n in [1..40]]; // Vincenzo Librandi, Oct 13 2015
(SageMath) [2*(2*chebyshev_U(n, 3) - chebyshev_U(n-1, 3)) for n in (0..30)] # G. C. Greubel, Jun 28 2022

Crossrefs

Cf. A001109, A038761, A048654.

Sequence in context: A121187 A011789 A047039 * A199033 A370695 A086682

Adjacent sequences: A100522 A100523 A100524 * A100526 A100527 A100528

Keyword

easy,nonn

Author

Lambert Klasen (lambert.klasen(AT)gmx.de), Nov 24 2004

Status

approved