OFFSET
0,1
LINKS
Vincenzo Librandi and Indranil Ghosh, Table of n, a(n) for n = 0..1922
Sergio Falcon, The k-Fibonacci difference sequences, Chaos, Solitons & Fractals, Volume 87, June 2016, Pages 153-157.
Index entries for linear recurrences with constant coefficients, signature (3,1).
FORMULA
G.f.: (4-x) / (1-3*x-x^2). - Vincenzo Librandi, Feb 26 2017
a(n) = (2^(-n)*((3-sqrt(13))^n*(-5+2*sqrt(13)) + (3+sqrt(13))^n*(5+2*sqrt(13)))) / sqrt(13). - Colin Barker, Feb 26 2017
MATHEMATICA
LinearRecurrence[{3, 1}, {4, 11}, 28] (* Indranil Ghosh, Feb 26 2017 *)
RecurrenceTable[{a[0]==4, a[1]==11, a[n]==3 a[n-1] + a[n-2]}, a, {n, 40}] (* or *) CoefficientList[Series[(4 - x)/(1 - 3 x - x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Feb 26 2017 *)
PROG
(Magma) I:=[4, 11]; [n le 2 select I[n] else 3*Self(n-1)+Self(n-2): n in [1..40]]; // Vincenzo Librandi, Feb 26 2017
(PARI) Vec((4-x) / (1-3*x-x^2) + O(x^30)) \\ Colin Barker, Feb 26 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Feb 25 2017
STATUS
approved