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a(n) = b(n) + d(n), where b(n) = (n-th Lucas number > 3) and d(n) = (n-th non-Lucas number).
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%I #15 May 28 2019 03:23:09

%S 6,12,17,26,38,57,88,136,213,337,537,860,1383,2227,3592,5800,9372,

%T 15151,24501,39629,64106,103710,167791,271474,439236,710680,1149885,

%U 1860533,3010385,4870884,7881234,12752082,20633279,33385323,54018563,87403846,141422368

%N a(n) = b(n) + d(n), where b(n) = (n-th Lucas number > 3) and d(n) = (n-th non-Lucas number).

%F a(n) = A000204(n+3) + A090946(n+1). - _Michel Marcus_, Jul 30 2015

%t Module[{nn=40,lnos,non,len},lnos=LucasL[Range[nn]];non= Complement[ Range[ 2*nn],lnos];len=Min[Length[lnos]-2,Length[non]];Total/@ Thread[ {Take[ lnos, {3,len+2}],Take[non,len]}]] (* _Harvey P. Dale_, Jul 29 2015 *)

%Y Cf. A000204, A090946.

%K nonn

%O 0,1

%A _Clark Kimberling_

%E Corrected and extended by _Harvey P. Dale_, Jul 29 2015