A256820 - OEIS

%I #7 Jan 21 2018 09:37:43

%S 64,128,256,512,956,1656,2693,4158,6153,8792,12202,16524,21914,28544,

%T 36603,46298,57855,71520,87560,106264,127944,152936,181601,214326,

%U 251525,293640,341142,394532,454342,521136,595511,678098,769563,870608,981972

%N Number of length n+5 0..1 arrays with at most two downsteps in every n consecutive neighbor pairs.

%C Row 5 of A256816.

%H R. H. Hardin, <a href="/A256820/b256820.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/120)*n^5 + (1/6)*n^4 + (175/24)*n^3 - (103/6)*n^2 + (747/10)*n - 30 for n>3.

%F Empirical g.f.: x*(64 - 256*x + 448*x^2 - 384*x^3 + 124*x^4 + 16*x^5 - 7*x^6 - 8*x^7 + 4*x^8) / (1 - x)^6. - _Colin Barker_, Jan 21 2018

%e Some solutions for n=4:

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

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

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

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

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

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

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

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

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

%Y Cf. A256816.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 10 2015