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A256822 Number of length n+7 0..1 arrays with at most two downsteps in every n consecutive neighbor pairs. 1

%I #7 Jan 21 2018 09:37:57

%S 256,512,1024,2048,3728,6192,9613,14168,20075,27566,36888,48304,62094,

%T 78556,98007,120784,147245,177770,212762,252648,297880,348936,406321,

%U 470568,542239,621926,710252,807872,915474,1033780,1163547,1305568

%N Number of length n+7 0..1 arrays with at most two downsteps in every n consecutive neighbor pairs.

%C Row 7 of A256816.

%H R. H. Hardin, <a href="/A256822/b256822.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/120)*n^5 + (1/4)*n^4 + (193/8)*n^3 - (169/4)*n^2 + (8323/15)*n - 1216 for n>5.

%F Empirical g.f.: x*(256 - 1024*x + 1792*x^2 - 1536*x^3 + 400*x^4 + 208*x^5 - 35*x^6 - 102*x^7 + 78*x^8 - 64*x^9 + 28*x^10) / (1 - x)^6. - _Colin Barker_, Jan 21 2018

%e Some solutions for n=4:

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

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

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

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

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

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

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

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

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

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

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

%Y Cf. A256816.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 10 2015

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Last modified July 15 10:33 EDT 2024. Contains 374332 sequences. (Running on oeis4.)