cp's OEIS Frontend

A256821 Number of length n+6 0..1 arrays with at most two downsteps in every n consecutive neighbor pairs.

%I A256821 #9 Jan 21 2018 09:37:50
%S A256821 128,256,512,1024,1888,3204,5088,7677,11120,15579,21230,28264,36888,
%T A256821 47326,59820,74631,92040,112349,135882,162986,194032,229416,269560,
%U A256821 314913,365952,423183,487142,558396,637544,725218,822084,928843,1046232
%N A256821 Number of length n+6 0..1 arrays with at most two downsteps in every n consecutive neighbor pairs.
%C A256821 Row 6 of A256816.
%H A256821 R. H. Hardin, <a href="/A256821/b256821.txt">Table of n, a(n) for n = 1..210</a>
%F A256821 Empirical: a(n) = (1/120)*n^5 + (5/24)*n^4 + (111/8)*n^3 - (701/24)*n^2 + (11767/60)*n - 253 for n>4.
%F A256821 Empirical g.f.: x*(128 - 512*x + 896*x^2 - 768*x^3 + 224*x^4 + 68*x^5 - 24*x^6 - 7*x^7 - 14*x^8 + 10*x^9) / (1 - x)^6. - _Colin Barker_, Jan 21 2018
%e A256821 Some solutions for n=4:
%e A256821 ..0....0....0....1....0....0....1....1....0....1....1....1....1....1....0....0
%e A256821 ..1....1....0....0....1....0....1....0....0....0....1....1....1....1....0....0
%e A256821 ..0....1....0....0....1....0....0....1....1....1....0....1....1....1....0....0
%e A256821 ..0....0....1....1....1....1....1....1....0....1....1....0....1....1....1....0
%e A256821 ..0....0....1....1....1....1....1....1....0....1....0....0....1....0....1....0
%e A256821 ..1....0....1....0....1....1....0....0....1....0....0....0....1....0....1....1
%e A256821 ..0....0....1....1....0....0....0....1....0....1....1....0....0....1....1....0
%e A256821 ..1....0....0....1....0....0....1....0....0....1....1....1....0....1....1....1
%e A256821 ..1....0....1....0....1....1....1....1....1....0....1....0....1....1....1....0
%e A256821 ..0....0....0....1....1....0....0....0....0....1....0....1....0....0....0....0
%Y A256821 Cf. A256816.
%K A256821 nonn
%O A256821 1,1
%A A256821 _R. H. Hardin_, Apr 10 2015