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%I #17 Nov 26 2022 03:33:53
%S 1,2,4,8,14,24,32,42,54,68,82,98,118,140,162,186,216,248,280,314,356,
%T 400,444,490,546,604,662,722,794,868,942,1018,1108,1200,1292,1386,
%U 1496,1608,1720,1834,1966,2100,2234,2370,2526,2684,2842,3002,3184,3368,3552
%N Number of length-n binary mesosome-avoiding strings.
%C A mesosome is a word of the form x x', where x' is a cyclic shift of x, different from x. A string is mesosome-avoiding if it has no subword (contiguous block) that is a mesosome.
%H Robert Cummings, Jeffrey Shallit and Paul Staadecker, <a href="https://arxiv.org/abs/2107.13813">Mesosome Avoidance</a>, arXiv:2107.13813 [cs.DM], 2021.
%F Let n = 4k + i for i = 0, 1, 2, 3 and n >= 5. Then:
%F a(4k ) = (4k^3 + 15k^2 + 41k - 12)/3;
%F a(4k + 1) = (4k^3 + 18k^2 + 50k )/3;
%F a(4k + 2) = (4k^3 + 21k^2 + 59k + 12)/3;
%F a(4k + 3) = (4k^3 + 24k^2 + 68k + 30)/3. [from 'Mesosome Avoidance', Theorem 2, eqn. (1), _Georg Fischer_, Nov 25 2022]
%e For n = 4 the only strings not counted are 0110 and 1001.
%K nonn
%O 0,2
%A _Jeffrey Shallit_, Feb 08 2021
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