A096796 a(n) = n for n <= 2; for n > 2, a(n) = 2a(n-1) - a(n - floor( 1/2 + sqrt(2n) )).

0, 1, 2, 3, 5, 8, 13, 23, 41, 74, 135, 257, 491, 941, 1808, 3481, 6827, 13397, 26303, 51665, 101522, 199563, 395645, 784463, 1555529, 3084755, 6117845, 12134168, 24068773, 47937983, 95480321, 190176179, 378796829, 754508903, 1502899961

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, A096824.

Cf. A083920, A003056.

Programs

Haskell

a096796 n = a096796_list !! n
a096796_list = 0 : 1 : zipWith (-)
   (map (* 2) $ tail a096796_list) (map a096796 $ tail a083920_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[2n]] ]]; Table[ a[n], {n, 0, 35}] (* Robert G. Wilson v *)

PARI

{m=35;v=vector(m+1);for(n=0,m,if(n<=2,a=n,k=n-floor(1/2+sqrt(2*n));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