A173495 a(n) = Lucas(n) - floor(Lucas(n)/2).

1, 1, 2, 2, 4, 6, 9, 15, 24, 38, 62, 100, 161, 261, 422, 682, 1104, 1786, 2889, 4675, 7564, 12238, 19802, 32040, 51841, 83881, 135722, 219602, 355324, 574926, 930249, 1505175, 2435424, 3940598, 6376022, 10316620, 16692641, 27009261, 43701902, 70711162

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

Cf. A000032, A001077.

Sequence in context: A234961 A018061 A304778 * A376195 A166289 A071058

Adjacent sequences: A173492 A173493 A173494 * A173496 A173497 A173498

Keyword

nonn

Author

Roger L. Bagula, Nov 23 2010

Status

approved