OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-2,-3).
FORMULA
G.f.: x/((1-3*x)*(1-x-x^2)).
a(n) = (1/5)*(3^(n+1) - Lucas(n+2)).
a(n) = 4*a(n-1) - 2*a(n-2) - 3*a(n-3).
a(n) = A101220(3, 3, n). - Ross La Haye, Jan 28 2005
a(n) = a(n-1) + a(n-2) + 3^(n-1) for n > 1, with a(0) = 0, a(1) = 1. - Ross La Haye, Aug 20 2005
a(n) = 3*a(n-1) + Fibonacci(n), where a(0) = 0. - Taras Goy, Mar 24 2019
MATHEMATICA
LinearRecurrence[{4, -2, -3}, {0, 1, 4}, 40] (* Vincenzo Librandi, Jun 24 2012 *)
Table[(3^(n+1) -LucasL[n+2])/5, {n, 0, 40}] (* Vladimir Reshetnikov, Sep 27 2016 *)
PROG
(PARI) a(n)=(3^(n+1)-fibonacci(n+1)-fibonacci(n+3))/5 \\ Charles R Greathouse IV, Jun 28 2011
(Magma) I:=[0, 1, 4]; [n le 3 select I[n] else 4*Self(n-1)-2*Self(n-2) -3*Self(n-3): n in [1..41]]; // Vincenzo Librandi, Jun 24 2012
(SageMath) [(3^(n+1) -lucas_number2(n+2, 1, -1))/5 for n in range(41)] # G. C. Greubel, Feb 09 2023
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 19 2004
STATUS
approved