OFFSET
1,5
COMMENTS
See also similar sequence A130578.
Numbers whose Zeckendorf representation is a prefix of 100100100... . - Jeffrey Shallit, Jun 29 2024
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,1,-1,-1).
FORMULA
G.f.: x^4*(1+x)/((1-x)(1+x+x^2)(1-x-x^2)). - Alois P. Heinz, Dec 13 2011
a(n) = F(n) - ceiling(F(n-1)/2) - ceiling(F(n-2)/2). - Chunqing Liu, Aug 21 2023
MAPLE
a:= n-> (Matrix(5, (i, j)-> `if`(i=j-1, 1, `if`(i=5,
[-1, -1, 1, 1, 1][j], 0)))^n. <<-1, 0, 0, 0, 1>>)[1, 1]:
seq(a(n), n=1..50); # Alois P. Heinz, Dec 13 2011
MATHEMATICA
CoefficientList[Series[x^3*(1+x)/((1-x)(1+x+x^2)(1-x-x^2)), {x, 0, 30}], x] (* Vincenzo Librandi, Mar 20 2012 *)
PROG
(Magma) [IsOdd(Fibonacci(n)) select (Fibonacci(n)-1)/2 else Fibonacci(n)/2-1: n in [1..41]]; // Bruno Berselli, Dec 14 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Giovanni Teofilatto, Dec 06 2011
STATUS
approved