login
a(n) = ((n+1)-st Lucas number) - (n-th non-Lucas number).
1

%I #15 Jun 20 2019 09:09:54

%S -2,-2,-1,2,8,17,34,62,108,183,305,502,823,1343,2185,3548,5754,9324,

%T 15101,24449,39575,64049,103651,167729,271410,439170,710612,1149815,

%U 1860461,3010311,4870808,7881156

%N a(n) = ((n+1)-st Lucas number) - (n-th non-Lucas number).

%H G. C. Greubel, <a href="/A014243/b014243.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = A000032(n+1) - A057854(n) for n >= 1. - _Michel Marcus_, May 28 2019

%e For example, a(5) = A000032(6) - A057854(5) = 18-10 = 8.

%t b:= Complement[Range[1, 100], LucasL[Range[20]]]; Table[LucasL[n+1] - b[[n+1]], {n,1,40}] (* _G. C. Greubel_, Jun 19 2019 *)

%Y Cf. A000032, A057854.

%K sign

%O 1,1

%A _Clark Kimberling_

%E Edited by _N. J. A. Sloane_, May 28 2019