OFFSET
0,2
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
Martin Burtscher, Igor Szczyrba, Rafał Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (2,2).
FORMULA
G.f.: 3x/(1 - 2x - 2x^2).
a(n) = lower left term of [1,1; 3,1]^n. - Gary W. Adamson, Mar 12 2008
MATHEMATICA
CoefficientList[Series[3x/(1-2x-2x^2), {x, 0, 25}], x]
s = Sqrt[3]; a[n_] := Simplify[s*((1 + s)^n - (1 - s)^n)/2]; Array[a, 30, 0] (* or *)
LinearRecurrence[{2, 2}, {0, 3}, 31] (* Robert G. Wilson v, Aug 07 2018 *)
PROG
(Haskell)
a083337 n = a083337_list !! n
a083337_list =
0 : 3 : map (* 2) (zipWith (+) a083337_list (tail a083337_list))
-- Reinhard Zumkeller, Oct 15 2011
(PARI) apply( a(n)=([1, 1; 3, 1]^n)[2, 1], [0..30]) \\ or: ([2, 2; 1, 0]^n)[2, 1]*3. - M. F. Hasler, Aug 06 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Mario Catalani (mario.catalani(AT)unito.it), Apr 29 2003
EXTENSIONS
Edited and definition completed by M. F. Hasler, Aug 06 2018
STATUS
approved