OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,1,-1,-1).
FORMULA
G.f.: (1-2*x^3)/[(1-x)*(1+x+x^2)*(1-x-x^2)].
a(n) = ceiling(Lucas(n)/2).
a(3n) = A001077(n). - Christopher Hohl, Aug 19 2021
MAPLE
a:= n-> (<<0|1|0|0|0>, <0|0|1|0|0>, <0|0|0|1|0>, <0|0|0|0|1>,
<-1|-1|1|1|1>>^n. <<1, 1, 2, 2, 4>>)[1, 1]:
seq(a(n), n=0..50); # Alois P. Heinz, Feb 17 2013
MATHEMATICA
l[0] = 2; l[1] = 1; l[n_] := l[n] = l[n - 1] + l[n - 2]; Table[l[n] - Floor[l[n]/2], {n, 0, 30}]
Table[Ceiling[LucasL[n]/2], {n, 0, 39}] (* Jean-François Alcover, Feb 17 2014 *)
CoefficientList[Series[(1 - 2 x^3)/((1 - x) (1 + x + x^2) (1 - x - x^2)), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 19 2014 *)
PROG
(Magma) [Ceiling(Lucas(n)/2): n in [0..40]]; // Vincenzo Librandi, Feb 19 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Nov 23 2010
STATUS
approved