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%I #9 Jan 11 2020 19:51:46
%S 1,3,7,16,33,35,47,61
%N a(n) is the maximum possible length of a sequence consisting of integers [0..n-1] such that no two nonempty adjacent segments of the same length have the same sum modulo n.
%C The original source for this sequence was the problem 'perlbrac' in the 2009 USACO Holiday Contest (http://ace.delos.com/HOL09) which asked contestants to find the longest sequences of this type that they possibly could. a(n) is the upper bound on the length of such a sequence for a given n.
%F Replacing each element x of a solution by ((a x + b) mod n) also gives a solution if gcd(a,n) = 1. - _Bert Dobbelaere_, Apr 18 2019
%e For example, in the sequence 0, 1, 2, 1, 0, 1, 2 (length 7) consisting of integers in the range [0..2], no two adjacent segments of equal length (e.g., 0, 1, 2 and 1, 0, 1) have the same sum modulo 3. There is also no longer sequence with this property, hence a(3) = 7.
%e From _Bert Dobbelaere_, Apr 18 2019: (Start)
%e Lexicographically earliest solutions represented as digit strings.
%e n a(n)
%e 1 1 0
%e 2 3 010
%e 3 7 0102010
%e 4 16 0130102013101201
%e 5 33 010214243213143040102142432131430
%e 6 35 01024021240241402401024021240241402
%e 7 47 01021614636032312426404301021614636032312426404
%e 8 61 0120135461316135364357463523745020571465756571764713467127313
%e (End)
%K hard,more,nonn
%O 1,2
%A Brian Bi (bbi5291(AT)gmail.com), Jun 19 2009
%E Definition and source corrected by Brian Bi (bbi5291(AT)gmail.com), Sep 19 2009
%E a(7)-a(8) from _Bert Dobbelaere_, Apr 18 2019