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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. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 25 16:31 EDT 2017. Contains 292499 sequences.