A345380 Number of Jacobsthal-Lucas numbers m <= n.

0, 1, 2, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7

Offset

0,3

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 5.6, pp. 35, Table 7.

Example

a(0)=0 since the least term in A014551 is 1.
a(1)=1 since A014551(0) = 2 is followed in that sequence by 1.
a(k)=2 for 2 <= k <= 4 since the first terms of A014551 are {2, 1, 5}.

Mathematica

Block[{a = 1, b = -2, 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 *)
{0}~Join~Accumulate@ ReplacePart[ConstantArray[0, Last[#]], Map[# -> 1 &, #]] &@ LinearRecurrence[{1, 2}, {2, 1}, 8] (* Michael De Vlieger, Jun 16 2021 *)

Crossrefs

Cf. A014551, A108852 (Fibonacci), A130245 (Lucas), A130253.

Sequence in context: A108504 A036468 A334051 * A367128 A028829 A130855

Adjacent sequences: A345377 A345378 A345379 * A345381 A345382 A345383

Keyword

nonn,easy

Author

Ovidiu Bagdasar, Jun 16 2021

Status

approved