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A255997 Number of length n+6 0..1 arrays with at most one downstep in every n consecutive neighbor pairs. 1

%I #7 Jan 26 2018 06:15:34

%S 128,256,354,451,568,705,854,1016,1192,1383,1590,1814,2056,2317,2598,

%T 2900,3224,3571,3942,4338,4760,5209,5686,6192,6728,7295,7894,8526,

%U 9192,9893,10630,11404,12216,13067,13958,14890,15864,16881,17942,19048,20200

%N Number of length n+6 0..1 arrays with at most one downstep in every n consecutive neighbor pairs.

%C Row 6 of A255992.

%H R. H. Hardin, <a href="/A255997/b255997.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/6)*n^3 + 3*n^2 + (533/6)*n + 28 for n>4.

%F Empirical g.f.: x*(128 - 256*x + 98*x^2 + 59*x^3 - 8*x^4 - 21*x^5 - 8*x^6 + 9*x^7) / (1 - x)^4. - _Colin Barker_, Jan 26 2018

%e Some solutions for n=4:

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

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

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

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

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

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

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

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

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

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

%Y Cf. A255992.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 13 2015

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Last modified June 20 05:29 EDT 2024. Contains 373512 sequences. (Running on oeis4.)