A255113 - OEIS

%I #8 Jan 24 2018 14:25:25

%S 2187,5157,7498,10125,14001,19263,25578,33063,41851,52092,63954,77624,

%T 93309,111237,131658,154845,181095,210730,244098,281574,323561,370491,

%U 422826,481059,545715,617352,696562,783972,880245,986081,1102218,1229433

%N Number of length n+6 0..2 arrays with at most one downstep in every n consecutive neighbor pairs.

%C Row 6 of A255107.

%H R. H. Hardin, <a href="/A255113/b255113.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/120)*n^5 + (3/8)*n^4 + (149/24)*n^3 + (2521/8)*n^2 + (56417/60)*n + 385 for n>4.

%F Empirical g.f.: x*(2187 - 7965*x + 9361*x^2 - 1248*x^3 - 4614*x^4 + 1405*x^5 + 1230*x^6 + 564*x^7 - 1354*x^8 + 435*x^9) / (1 - x)^6. - _Colin Barker_, Jan 24 2018

%e Some solutions for n=4:

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

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

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

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

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

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

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

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

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

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

%Y Cf. A255107.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 14 2015