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A215229 Number of length-6 0..k arrays connected end-around, with no sequence of L<n elements immediately followed by itself (periodic "squarefree"). 1

%I #13 Jul 23 2018 08:44:22

%S 0,18,408,2940,12600,40110,105168,240408,496080,945450,1690920,

%T 2870868,4667208,7313670,11104800,16405680,23662368,33413058,46299960,

%U 63081900,84647640,112029918,146420208,189184200,241878000,306265050,384333768

%N Number of length-6 0..k arrays connected end-around, with no sequence of L<n elements immediately followed by itself (periodic "squarefree").

%C Row 6 of A215228.

%H R. H. Hardin, <a href="/A215229/b215229.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^6 - 6*n^4 + 5*n^3 + 5*n^2 - 5*n.

%F Conjectures from _Colin Barker_, Jul 23 2018: (Start)

%F G.f.: 6*x^2*(3 + 47*x + 77*x^2 - 7*x^3) / (1 - x)^7.

%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

%F (End)

%e Some solutions for n=5:

%e ..2....1....5....4....3....0....4....5....1....4....2....5....3....1....1....5

%e ..0....3....2....2....1....4....1....4....2....1....3....3....4....4....4....1

%e ..5....4....3....3....2....1....2....2....3....3....1....5....5....1....0....4

%e ..0....5....0....2....4....5....4....0....2....2....3....0....0....5....4....2

%e ..4....1....1....0....0....4....5....4....0....5....4....2....1....2....3....3

%e ..1....2....3....2....5....3....2....3....5....3....5....0....5....0....5....4

%Y Cf. A215228.

%K nonn

%O 1,2

%A _R. H. Hardin_, Aug 06 2012

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)