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%I #10 Mar 29 2022 03:40:37
%S 1,1,1,2,2,3,3,3,4,5,5,5,6,6,7,7,8,9,9,9,10,10,11,11,11,12,13,13,13,
%T 14,15,16,16,16,17,18,18,18,18,19,20,21,21,21,21,22,22,23,23,24,25,25,
%U 25,26,26,27,27,28,29,30,30,30,31,32,32,32,32,33,35,35
%N a(1) = a(2) = a(3) = 1, a(n) = a(n-2-a(n-2)) + a(n-1-a(n-3)) for n>3.
%C First numbers not occurring: 62, 66, 75, 79, 114, 123, ... .
%H Reinhard Zumkeller, <a href="/A226222/b226222.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HofstadtersQ-Sequence.html">Hofstadter's Q-Sequence</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Hofstadter_sequence">Hofstadter sequence</a>
%H <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>
%F a(n) = a(n-2 - a(n-2)) + a(n-1 - a(n-3)), with a(1) = a(2) = a(3) = 1.
%t a[n_]:= a[n]= If[n<4, 1, a[n-2 -a[n-2]] + a[n-1 -a[n-3]]];
%t Table[a[n], {n, 80}] (* _G. C. Greubel_, Mar 28 2022 *)
%o (Haskell)
%o a226222 n = a226222_list !! (n-1)
%o a226222_list = 1 : 1 : 1 : zipWith (+)
%o (map a226222 $ zipWith (-) [3..] a226222_list)
%o (map a226222 $ zipWith (-) [2..] $ tail a226222_list)
%o -- _Reinhard Zumkeller_, May 31 2013
%o (Sage)
%o @CachedFunction
%o def a(n): # A226222
%o if (n<4): return 1
%o else: return a(n-2-a(n-2)) + a(n-1-a(n-3))
%o [a(n) for n in (1..80)] # _G. C. Greubel_, Mar 28 2022
%Y Cf. A005185, A046699, A063892, A070867.
%K nonn,look
%O 1,4
%A _Reinhard Zumkeller_, May 31 2013
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