A345377 Number of terms m <= n, where m is a term in A006190.
1, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 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, 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, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5
Offset: 0
Examples
a(0)=1, since A006190(0) = 0 and A006190(1) = 1.
a(1)=a(2)=2 since 0 and 1 are the terms in A006190 that do not exceed 1 and 2, respectively.
a(k)=3 for 3 <= k <= 9 since the first terms of A006190 are {0, 1, 3, 10}.
Links
- Michael De Vlieger, Table of n, a(n) for n = 0..10000
- Dorin Andrica, Ovidiu Bagdasar, and George Cătălin Tųrcąs, On some new results for the generalised Lucas sequences, An. Şt. Univ. Ovidius Constanţa (Romania, 2021) Vol. 29, No. 1, 17-36. See Section 5.3, pp. 33, Table 4.
Programs
-
Mathematica
Block[{a = 3, b = -1, nn = 105, u, v = {}}, u = {0, 1}; Do[AppendTo[u, Total[{-b, a} u[[-2 ;; -1]]]]; AppendTo[v, Count[u, _?(# <= i &)]], {i, nn}]; {Boole[First[u] <= 0]}~Join~v] (* or *) Accumulate@ ReplacePart[ConstantArray[0, Last[#]], Map[# -> 1 &, # + 1]] &@ Fibonacci[Range[0, 5], 3] (* Michael De Vlieger, Jun 16 2021 *)
Comments