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a(n) = b(n) + d(n), where b(n) = (n-th Lucas number) and d(n) = (n-th non-Fibonacci number).
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%I #16 Apr 26 2020 11:48:44

%S 5,9,11,16,21,29,41,61,91,139,216,340,540,863,1386,2230,3595,5803,

%T 9375,15154,24504,39632,64109,103713,167793,271476,439239,710683,

%U 1149888,1860536,3010388,4870887,7881237,12752085,20633282,33385326

%N a(n) = b(n) + d(n), where b(n) = (n-th Lucas number) and d(n) = (n-th non-Fibonacci number).

%H Harvey P. Dale, <a href="/A023484/b023484.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = A000032(n+1) + A001690(n+1). - _R. J. Mathar_, Feb 01 2019

%t Module[{nn=40,nf},nf=Take[Complement[Range[2nn],Fibonacci[Range[nn]]],nn];Total/@Thread[{LucasL[Range[nn]],nf}]] (* _Harvey P. Dale_, Apr 26 2020 *)

%Y Cf. A000032, A001690.

%K nonn

%O 0,1

%A _Clark Kimberling_

%E a(14) onward corrected by _Sean A. Irvine_, Jun 04 2019