A192484 Shifts left under XOR-convolution: a(n) = Sum_{k=0..n-1} a(k) XOR a(n-k-1) for n>1 with a(0)=1, a(1)=2.

1, 2, 6, 14, 38, 102, 294, 854, 2566, 7622, 22790, 68166, 204678, 613318, 1839750, 5518310, 16553798, 49656774, 148968774, 446888518, 1340652486, 4021929542, 12065804486, 36197270598, 108591619654, 325774522822, 977323956550

Offset: 0

Author

Paul D. Hanna, Jul 02 2011

Keywords

• nonn

Comments

Limit a(n+1)/a(n) = 3.

Examples

			Given a(0)=1, a(1)=2, illustrate XOR convolution for the initial terms.
a(2) = 1 XOR 2 + 2 XOR 1 = 3 + 3 = 6;
a(3) = 1 XOR 6 + 2 XOR 2 + 6 XOR 1 = 7 + 0 + 7 = 14;
a(4) = 1 XOR 14 + 2 XOR 6 + 6 XOR 2 + 14 XOR 1 = 15 + 4 + 4 + 15 = 38; ...
		

Links

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

Crossrefs

Cf. variant: A007462.

Cf. A199770.

Programs

Haskell

import Data.Bits (xor)
a192484 n = a192484_list !! n
a192484_list = 1 : 2 : f [2,1] where
   f xs = y : f (y : xs) where
     y = sum $ zipWith xor xs $ reverse xs :: Integer
-- Reinhard Zumkeller, Jul 15 2012

PARI

{a(n)=if(n<2,n+1,sum(k=0,n-1,bitxor(a(k),a(n-k-1))))}