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a(1) = a(2) = 1; a(n) = <>(a(n-1)) + <>(a(n-2)) for n > 2, where <>(k) denotes the concatenation of k with itself.
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%I #2 Feb 11 2014 19:05:28

%S 1,1,22,2233,22334455,2233445544666688,

%T 22334455446666884466891067001143,

%U 2233445544666688446689106700114344668910893333766700336611667831

%N a(1) = a(2) = 1; a(n) = <>(a(n-1)) + <>(a(n-2)) for n > 2, where <>(k) denotes the concatenation of k with itself.

%e a(4) = <>(a(3)) + <>(a(2)) = <>(22) + <>(1) = 2222 + 11= 2233.

%K base,nonn

%O 1,3

%A _Joseph L. Pe_, Apr 12 2002