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A117548 Values of n for which there exist d(1),...,d(n), each in {0,1,2} and an r in {1,2} such that Sum_{i=1..n-k} d(i)*d(i+k) == r (mod 3) for all k=0..n-1. (Such a sequence is called a very(3,r) sequence. See the link.).

%I A117548 #17 Sep 13 2024 00:39:17
%S A117548 1,2,5,6,7,12,14,17,20,24
%N A117548 Values of n for which there exist d(1),...,d(n), each in {0,1,2} and an r in {1,2} such that Sum_{i=1..n-k} d(i)*d(i+k) == r (mod 3) for all k=0..n-1. (Such a sequence is called a very(3,r) sequence. See the link.).
%C A117548 Theorem. Let a be a very(3,r) sequence of length n, for r=1 or 2 and let z be a sequence of n-1 0's. Then az(2a) is a very(3,3-r) sequence of length 3n-1, where 2a denotes the sequence {2a(i) mod 3, i=1..n}.
%H A117548 John W. Layman, <a href="http://intranet.math.vt.edu/people/layman/sequences/very_br.htm">On A Generalization of Very Odd Sequences</a>
%e A117548 For the sequence d=112102 we get Sum_{i=1..n-k} d(i)*d(i+k) = {11,5,5,5,2,2} = {2,2,2,2,2,2} (mod 3) for k=0..5, so 6 is a term of the sequence.
%Y A117548 Cf. A053006, A117549.
%K A117548 nonn,more
%O A117548 1,2
%A A117548 _John W. Layman_, Mar 28 2006