|
%I #11 Jun 23 2021 10:51:19
%S 0,0,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,
%T 4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,
%U 5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5
%N Number of terms m <= n, where m is a term in the bisection of Lucas numbers (A005248).
%H Michael De Vlieger, <a href="/A345379/b345379.txt">Table of n, a(n) for n = 0..10000</a>
%H Dorin Andrica, Ovidiu Bagdasar, and George Cătălin Tųrcąs, <a href="https://doi.org/10.2478/auom-2021-0002">On some new results for the generalised Lucas sequences</a>, An. Şt. Univ. Ovidius Constanţa (Romania, 2021) Vol. 29, No. 1, 17-36. See Section 5.4, pp. 33-34, Table 4.
%e a(0)=a(1)=0, since the least term in A005248 is 2.
%e a(2)=1 since A005248(0) = 2 is followed in that sequence by 3.
%e a(k)=3 for 3 <= k <= 6 since the first terms of A005248 are {0, 2, 3, 7}.
%t Block[{a = 3, b = 1, nn = 105, u, v = {}}, u = {2, a}; Do[AppendTo[u, Total[{-b, a} u[[-2 ;; -1]]]]; AppendTo[v, Count[u, _?(# <= i &)]], {i, nn}]; {Boole[First[u] <= 0]}~Join~v] ] (* or *)
%t {0}~Join~Accumulate@ ReplacePart[ConstantArray[0, Last[#]], Map[# -> 1 &, #]] &@ LucasL@ Range[0, 10, 2] (* _Michael De Vlieger_, Jun 16 2021 *)
%Y Cf. A005248, A108852 (Fibonacci), A130245 (Lucas), A130260.
%K nonn,easy
%O 0,4
%A _Ovidiu Bagdasar_, Jun 16 2021
|
