A153819 Linear recurrence with a(n) = 3a(n-1) - a(n-2) + 2 = 4a(n-1) - 4a(n-2) + a(n-3). Full sequence for A153466.

16, 34, 88, 232, 610, 1600, 4192, 10978, 28744, 75256, 197026, 515824, 1350448, 3535522, 9256120, 24232840, 63442402, 166094368, 434840704, 1138427746, 2980442536, 7802899864, 20428257058, 53481871312, 140017356880, 366570199330, 959693241112, 2512509524008

Offset

0,1

Comments

a(n) mod 9 = 7.

A two-way infinite sequence with a(-n) = a(n-1).

Links

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

Index entries for linear recurrences with constant coefficients, signature (4,-4,1).

Formula

G.f.: 2*(8-15*x+8*x^2)/((1-x)*(1-3*x+x^2)). - Jaume Oliver Lafont, Aug 30 2009

a(n) = 2*A153873(n) = 18*Fibonacci(2*n+1)-2.

a(n) = (2^(-n)*(-5*2^(1+n)-9*(3-sqrt(5))^n*(-5+sqrt(5))+9*(3+sqrt(5))^n*(5+sqrt(5))))/5. - Colin Barker, Nov 02 2016

Mathematica

LinearRecurrence[{4, -4, 1}, {16, 34, 88} , 100] (* G. C. Greubel, Jun 18 2016 *)

Prog

(Magma) [18*Fibonacci(2*n+1)-2: n in [0..30]]; // Vincenzo Librandi, Jun 19 2016
(PARI) Vec(2*(8-15*x+8*x^2)/((1-x)*(1-3*x+x^2)) + O(x^30)) \\ Colin Barker, Nov 02 2016

Crossrefs

Sequence in context: A132760 A209377 A203446 * A185459 A279712 A228800

Adjacent sequences: A153816 A153817 A153818 * A153820 A153821 A153822

Keyword

nonn,easy

Author

Paul Curtz, Jan 02 2009

Extensions

Edited by Charles R Greathouse IV, Oct 05 2009

Status

approved