cp's OEIS Frontend

A116590 a(0)=1; a(n)=b(n+2)+b(n), where b(n)=A005185(n) is the Hofstadter Q-sequence: b(1)=b(2)=1; b(n)=b(n-b(n-1))+b(n-b(n-2)) for n > 2.

%I A116590 #16 Dec 13 2017 02:42:29
%S A116590 1,3,4,5,7,8,9,11,11,12,14,14,16,18,17,20,20,21,23,23,24,24,28,26,30,
%T A116590 30,30,32,32,36,33,37,37,38,39,41,41,41,44,44,45,47,47,48,48,48,56,48,
%U A116590 57,54,53,56,58,56,58,62,58,64,62,64,64,72,65,71,71,66,71,74,73,76,78,77
%N A116590 a(0)=1; a(n)=b(n+2)+b(n), where b(n)=A005185(n) is the Hofstadter Q-sequence: b(1)=b(2)=1; b(n)=b(n-b(n-1))+b(n-b(n-2)) for n > 2.
%C A116590 A similar definition applied to the Fibonacci sequence (A000045) leads to the Lucas sequence (A000032).
%H A116590 Reinhard Zumkeller, <a href="/A116590/b116590.txt">Table of n, a(n) for n = 0..10000</a>
%F A116590 a(n) = A005185(n+2) + A005185(n) for n>=1.
%p A116590 b:=proc(n) option remember; if n<=2 then 1 else b(n-b(n-1))+b(n-b(n-2)): fi: end: a[0]:=1: for n from 1 to 71 do a[n]:=b(n)+b(n+2) od: seq(a[n],n=0..71);
%t A116590 F[0] = 0; F[1] = 1; F[2] = 1; F[n_] := F[n] = F[n - F[n - 1]] + F[n - F[n - 2]] L[0] = 1; L[n_] := L[n] = F[n - 1] + F[n + 1]
%t A116590 Table[L[n], {n, 1, 200}]
%o A116590 (Haskell)
%o A116590 a116590 n = a116590_list !! n
%o A116590 a116590_list = 1 : zipWith (+) a005185_list (drop 2 a005185_list)
%o A116590 -- _Reinhard Zumkeller_, Apr 25 2012
%Y A116590 Cf. A000032, A005185.
%K A116590 nonn,look
%O A116590 0,2
%A A116590 _Roger L. Bagula_, Mar 27 2006
%E A116590 Edited by _N. J. A. Sloane_, Apr 15 2006