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

0, 1, 2, 3, 4, 6, 9, 14, 24, 42, 75, 136, 258, 492, 942, 1809, 3482, 6828, 13398, 26304, 51666, 101523, 199564, 395646, 784464, 1555530, 3084756, 6117846, 12134169, 24068774, 47937984, 95480322, 190176180, 378796830, 754508904, 1502899962

Offset: 0

Author

N. J. A. Sloane, Aug 17 2004

Keywords

• nonn
• easy

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A005318, A096796.

Cf. A122797, A003056.

Programs

Haskell

a096824 n = a096824_list !! n
a096824_list = 0 : 1 : 2 : zipWith (-)
   (map (* 2) $ drop 2 a096824_list) (map a096824 $ tail a122797_list)
-- Reinhard Zumkeller, Feb 12 2012

Mathematica

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 *)

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

Extensions

More terms from Klaus Brockhaus and Robert G. Wilson v, Aug 20 2004