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a(n) = a(n-1) XOR (a(n-1) + a(n-2)), with a(1)=1, a(2)=3, where XOR is the binary exclusive OR operation.
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%I #6 May 11 2014 22:50:36

%S 1,3,7,13,25,63,103,193,489,835,1647,4061,6545,12543,31343,53505,

%T 105073,258307,424567,790797,2005641,3420447,6748855,16634209,

%U 26811769,51377059,128377535,219165917,430383937,1058044767,1739056639

%N a(n) = a(n-1) XOR (a(n-1) + a(n-2)), with a(1)=1, a(2)=3, where XOR is the binary exclusive OR operation.

%e a(3) = 7 since 3 XOR (3+1) = 3 XOR 4 = 7.

%e a(4) = 13 since 7 XOR (7+3) = 7 XOR 10 = 13.

%e a(5) = 25 since 13 XOR (13+7) = 13 XOR 20 = 25.

%e The binary expansions of a(n) form a triangle (listed with ones place in leftmost column):

%e 1,

%e 1,1,

%e 1,1,1,

%e 1,0,1,1,

%e 1,0,0,1,1,

%e 1,1,1,1,1,1,

%e 1,1,1,0,0,1,1,

%e 1,0,0,0,0,0,1,1,

%e 1,0,0,1,0,1,1,1,1,

%e 1,1,0,0,0,0,1,0,1,1,

%e 1,1,1,1,0,1,1,0,0,1,1,

%e 1,0,1,1,1,0,1,1,1,1,1,1,...

%o (PARI) a(n)=if(n==1,1,if(n==2,3,bitxor(a(n-1),a(n-1)+a(n-2))))

%Y Cf. A099811.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Oct 26 2004