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 A263710 Number of length n arrays of permutations of 0..n-1 with each element moved by -1 to 1 places and every four consecutive elements having its maximum within 4 of its minimum. 3

%I #13 Oct 21 2022 14:32:48

%S 1,2,3,5,8,11,17,25,37,57,84,127,191,284,429,641,961,1445,2161,3246,

%T 4867,7293,10948,16407,24609,36913,55337,83009,124472,186655,279951,

%U 419784,629561,944129,1415809,2123305,3184145,4775114,7161091,10738981,16104880

%N Number of length n arrays of permutations of 0..n-1 with each element moved by -1 to 1 places and every four consecutive elements having its maximum within 4 of its minimum.

%H R. H. Hardin, <a href="/A263710/b263710.txt">Table of n, a(n) for n = 1..210</a>

%H Michael A. Allen, <a href="https://arxiv.org/abs/2210.08167">Combinations without specified separations and restricted-overlap tiling with combs</a>, arXiv:2210.08167 [math.CO], 2022.

%F Empirical: a(n) = a(n-1) + a(n-3) - a(n-4) + 2*a(n-5) - a(n-6) + a(n-7).

%F Empirical g.f.: x*(1 - x + x^2)*(1 + 2*x + 2*x^2 + x^3 + x^4) / (1 - x - x^3 + x^4 - 2*x^5 + x^6 - x^7). - _Colin Barker_, Jan 02 2019

%e Some solutions for n=7:

%e ..0....0....0....0....1....0....0....1....1....0....1....1....0....0....1....0

%e ..2....1....2....2....0....1....1....0....0....1....0....0....1....1....0....1

%e ..1....2....1....1....2....2....2....2....2....3....2....3....2....3....3....3

%e ..3....3....3....4....3....3....4....4....4....2....3....2....4....2....2....2

%e ..4....4....5....3....4....4....3....3....3....4....4....4....3....4....4....5

%e ..5....6....4....5....6....5....5....6....5....5....5....6....6....6....5....4

%e ..6....5....6....6....5....6....6....5....6....6....6....5....5....5....6....6

%Y Column 1 of A263714.

%K nonn

%O 1,2

%A _R. H. Hardin_, Oct 24 2015

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Last modified October 4 22:13 EDT 2023. Contains 365888 sequences. (Running on oeis4.)