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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.

%I A192484 #11 Jul 13 2013 12:04:12
%S A192484 1,2,6,14,38,102,294,854,2566,7622,22790,68166,204678,613318,1839750,
%T A192484 5518310,16553798,49656774,148968774,446888518,1340652486,4021929542,
%U A192484 12065804486,36197270598,108591619654,325774522822,977323956550
%N 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.
%C A192484 Limit a(n+1)/a(n) = 3.
%H A192484 Reinhard Zumkeller, <a href="/A192484/b192484.txt">Table of n, a(n) for n = 0..1000</a>
%e A192484 Given a(0)=1, a(1)=2, illustrate XOR convolution for the initial terms.
%e A192484 a(2) = 1 XOR 2 + 2 XOR 1 = 3 + 3 = 6;
%e A192484 a(3) = 1 XOR 6 + 2 XOR 2 + 6 XOR 1 = 7 + 0 + 7 = 14;
%e A192484 a(4) = 1 XOR 14 + 2 XOR 6 + 6 XOR 2 + 14 XOR 1 = 15 + 4 + 4 + 15 = 38; ...
%o A192484 (PARI) {a(n)=if(n<2,n+1,sum(k=0,n-1,bitxor(a(k),a(n-k-1))))}
%o A192484 (Haskell)
%o A192484 import Data.Bits (xor)
%o A192484 a192484 n = a192484_list !! n
%o A192484 a192484_list = 1 : 2 : f [2,1] where
%o A192484    f xs = y : f (y : xs) where
%o A192484      y = sum $ zipWith xor xs $ reverse xs :: Integer
%o A192484 -- _Reinhard Zumkeller_, Jul 15 2012
%Y A192484 Cf. variant: A007462.
%Y A192484 Cf. A199770.
%K A192484 nonn
%O A192484 0,2
%A A192484 _Paul D. Hanna_, Jul 02 2011