OFFSET
0,5
COMMENTS
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
Victoria Zhuravleva, Diophantine approximations with Fibonacci numbers, Journal de théorie des nombres de Bordeaux, 25 no. 2 (2013), p. 499-520. See Lemma 5.1.
Index entries for linear recurrences with constant coefficients, signature (1,0,1,1).
FORMULA
a(n) = a(n-1) + a(n-3) + a(n-4) for n>3, a(0)=0, a(1)=1, a(2)=1, a(3)=1.
G.f.: x/(1 - x - x^3 - x^4).
a(n) = Fibonacci(ceiling(n/2))*Fibonacci(floor(n/2+1)). - Alois P. Heinz, Jan 15 2024
MATHEMATICA
CoefficientList[Series[x/(1 - x - x^3 - x^4), {x, 0, 40}], x]
PROG
(Haskell)
a074677 n = a074677_list !! (n-1)
a074677_list = 0 : 1 : 1 : 1 : zipWith (+) a074677_list
(zipWith (+) (tail a074677_list) (drop 3 a074677_list))
-- Reinhard Zumkeller, Dec 28 2011
(Sage) [sum((-1)^(i+floor(n/2))*fibonacci(2*i+(1-(-1)^n)/2) for i in (0..floor(n/2))) for n in [0..50]]; # Bruno Berselli, Mar 15 2016
(Magma) [&+[(-1)^(i+Floor(n/2))*Fibonacci(2*i+(1-(-1)^n) div 2): i in [0..Floor(n/2)]]: n in [0..50]]; // Bruno Berselli, Mar 15 2016
(PARI) concat(0, Vec(x/((1+x^2)*(1-x-x^2)) + O(x^50))) \\ Colin Barker, Mar 15 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mario Catalani (mario.catalani(AT)unito.it), Aug 30 2002
STATUS
approved