cp's OEIS Frontend

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

%I A256822 #7 Jan 21 2018 09:37:57
%S A256822 256,512,1024,2048,3728,6192,9613,14168,20075,27566,36888,48304,62094,
%T A256822 78556,98007,120784,147245,177770,212762,252648,297880,348936,406321,
%U A256822 470568,542239,621926,710252,807872,915474,1033780,1163547,1305568
%N A256822 Number of length n+7 0..1 arrays with at most two downsteps in every n consecutive neighbor pairs.
%C A256822 Row 7 of A256816.
%H A256822 R. H. Hardin, <a href="/A256822/b256822.txt">Table of n, a(n) for n = 1..210</a>
%F A256822 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 A256822 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 A256822 Some solutions for n=4:
%e A256822 ..0....1....1....1....1....0....1....1....1....1....1....1....0....0....1....1
%e A256822 ..1....0....1....1....1....1....0....1....0....1....1....0....0....1....1....1
%e A256822 ..1....0....1....0....1....1....1....0....1....0....1....1....0....0....1....1
%e A256822 ..1....1....0....0....1....1....1....1....1....1....0....1....0....0....0....0
%e A256822 ..0....1....1....0....1....0....1....0....1....0....1....1....1....1....1....1
%e A256822 ..1....1....1....0....0....1....0....1....1....1....1....1....1....1....0....0
%e A256822 ..1....1....1....0....1....0....0....1....1....0....1....0....0....1....0....0
%e A256822 ..0....1....0....0....0....1....0....1....0....0....1....1....1....1....0....0
%e A256822 ..1....1....0....0....1....1....0....0....0....1....0....0....1....1....1....1
%e A256822 ..1....0....1....1....0....1....1....0....0....0....0....0....0....0....0....0
%e A256822 ..1....0....0....0....0....0....1....0....0....1....1....1....1....0....1....0
%Y A256822 Cf. A256816.
%K A256822 nonn
%O A256822 1,1
%A A256822 _R. H. Hardin_, Apr 10 2015