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A096824 a(n) = n for n <= 2; for n > 2, a(n) = 2a(n-1) - a(n - floor(1/2 + sqrt(2(n-1)))).

%I A096824 #13 Jul 26 2015 01:52:48
%S A096824 0,1,2,3,4,6,9,14,24,42,75,136,258,492,942,1809,3482,6828,13398,26304,
%T A096824 51666,101523,199564,395646,784464,1555530,3084756,6117846,12134169,
%U A096824 24068774,47937984,95480322,190176180,378796830,754508904,1502899962
%N A096824 a(n) = n for n <= 2; for n > 2, a(n) = 2a(n-1) - a(n - floor(1/2 + sqrt(2(n-1)))).
%H A096824 Reinhard Zumkeller, <a href="/A096824/b096824.txt">Table of n, a(n) for n = 0..1000</a>
%t A096824 a[n_] := a[n] = If[n < 3, a[n] = n, 2a[n - 1] - a[n - Floor[1/2 + Sqrt[2(n - 1)]]]]; Table[ a[n], {n, 0, 35}] (* _Robert G. Wilson v_, Aug 20 2004 *)
%o A096824 (PARI) {m=36;v=vector(m+1);for(n=0,m,if(n<=2,a=n,k=n-floor(1/2+sqrt(2*(n-1)));a=2*v[n]-v[k+1]);v[n+1]=a;print1(a,","))} \\ _Klaus Brockhaus_, Aug 20 2004
%o A096824 (Haskell)
%o A096824 a096824 n = a096824_list !! n
%o A096824 a096824_list = 0 : 1 : 2 : zipWith (-)
%o A096824    (map (* 2) $ drop 2 a096824_list) (map a096824 $ tail a122797_list)
%o A096824 -- _Reinhard Zumkeller_, Feb 12 2012
%Y A096824 Cf. A005318, A096796.
%Y A096824 Cf. A122797, A003056.
%K A096824 nonn,easy
%O A096824 0,3
%A A096824 _N. J. A. Sloane_, Aug 17 2004
%E A096824 More terms from _Klaus Brockhaus_ and _Robert G. Wilson v_, Aug 20 2004