Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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