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

Author

Paul Curtz, Jan 02 2009

Keywords

• nonn
• easy

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).

Programs

Magma

[18*Fibonacci(2*n+1)-2: n in [0..30]]; // Vincenzo Librandi, Jun 19 2016

Mathematica

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

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

Extensions

Edited by Charles R Greathouse IV, Oct 05 2009