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a(1)=1; for n > 1, a(n) is the length of the longest palindromic suffix of (a(1), ..., a(n-1)).
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%I #19 Jul 23 2019 15:32:01

%S 1,1,2,1,3,1,3,3,2,1,1,2,4,1,1,2,1,3,1,3,3,2,1,1,2,4,1,1,2,1,3,1,3,3,

%T 2,1,1,2,4,1,1,2,1,3,1,3,3,2,1,1,2,4,1,1,2,1,3,1,3,3,2,1,1,2,4,1,1,2,

%U 1,3,1,3,3,2,1,1,2,4,1,1,2,1,3,1,3,3,2

%N a(1)=1; for n > 1, a(n) is the length of the longest palindromic suffix of (a(1), ..., a(n-1)).

%C The sequence repeats after 13 terms.

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,0,1).

%F G.f.: (1 + x + 2*x^2 + x^3 + 3*x^4 + x^5 + 3*x^6 + 3*x^7 + 2*x^8 + x^9 + x^10 + 2*x^11 + 4*x^12)/(1 - x^13). - _Stefano Spezia_, Jul 21 2019

%e 1

%e [1], 1

%e [1 , 1], 2

%e 1 , 1 ,[2], 1

%e 1 ,[1 , 2 , 1], 3

%e 1 , 1 , 2 , 1 ,[3], 1

%e 1 , 1 , 2 ,[1 , 3 , 1], 3

%e 1 , 1 , 2 , 1 ,[3 , 1 , 3], 3

%e 1 , 1 , 2 , 1 , 3 , 1 ,[3 , 3], 2

%e 1 , 1 , 2 , 1 , 3 , 1 , 3 , 3 ,[2], 1

%e 1 , 1 , 2 , 1 , 3 , 1 , 3 , 3 , 2 ,[1], 1

%e 1 , 1 , 2 , 1 , 3 , 1 , 3 , 3 , 2 ,[1 , 1], 2

%e 1 , 1 , 2 , 1 , 3 , 1 , 3 , 3 ,[2 , 1 , 1 , 2], 4

%Y Cf. A220080.

%K nonn

%O 1,3

%A _Samuel B. Reid_, Jun 15 2019