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A258731 Number of length n+1 0..3 arrays with at most one downstep in every n consecutive neighbor pairs. 1

%I

%S 16,60,190,512,1212,2592,5115,9460,16588,27820,44928,70240,106760,

%T 158304,229653,326724,456760,628540,852610,1141536,1510180,1976000,

%U 2559375,3283956,4177044,5269996,6598660,8203840,10131792,12434752,15171497

%N Number of length n+1 0..3 arrays with at most one downstep in every n consecutive neighbor pairs.

%C Row 1 of A258730.

%H R. H. Hardin, <a href="/A258731/b258731.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/5040)*n^7 + (1/144)*n^6 + (73/720)*n^5 + (91/144)*n^4 + (179/90)*n^3 + (139/36)*n^2 + (568/105)*n + 4.

%F Empirical g.f.: x*(2 - x)*(8 - 30*x + 64*x^2 - 80*x^3 + 58*x^4 - 23*x^5 + 4*x^6) / (1 - x)^8. - _Colin Barker_, Jan 26 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Cf. A258730.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jun 08 2015

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Last modified May 19 04:20 EDT 2022. Contains 353826 sequences. (Running on oeis4.)