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A341277 Number of length-n binary mesosome-avoiding strings. 0
1, 2, 4, 8, 14, 24, 32, 42, 54, 68, 82, 98, 118, 140, 162, 186, 216, 248, 280, 314, 356, 400, 444, 490, 546, 604, 662, 722, 794, 868, 942, 1018, 1108, 1200, 1292, 1386, 1496, 1608, 1720, 1834, 1966, 2100, 2234, 2370, 2526, 2684, 2842, 3002, 3184, 3368, 3552 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=0..50.

Robert Cummings, Jeffrey Shallit and Paul Staadecker, Mesosome Avoidance, arXiv:2107.13813 [cs.DM], 2021.

FORMULA

a(4n) = 2n^3/3 - 3n^2/2 + 5n/6, n >= 2;

a(4n+1) = 2n^3/3 - n^2 + n/3, n >= 1;

a(4n+2) = 2n^3/3 - n^2/2 - n/6, n >= 1;

a(4n+3) = 2n^3/3 - 2n/3, n >= 1.

EXAMPLE

For n = 4 the only strings not counted are 0110 and 1001.

CROSSREFS

Sequence in context: A018153 A101687 A096461 * A049701 A005598 A290845

Adjacent sequences:  A341274 A341275 A341276 * A341278 A341279 A341280

KEYWORD

nonn

AUTHOR

Jeffrey Shallit, Feb 08 2021

STATUS

approved

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Last modified December 5 06:49 EST 2021. Contains 349535 sequences. (Running on oeis4.)