A255114 - OEIS

%I #8 Jan 24 2018 14:30:29

%S 6561,14849,19338,23463,29147,38010,49611,63075,78552,96210,116236,

%T 138837,164241,192698,224481,259887,299238,342882,391194,444577,

%U 503463,568314,639623,717915,803748,897714,1000440,1112589,1234861,1367994

%N Number of length n+7 0..2 arrays with at most one downstep in every n consecutive neighbor pairs.

%C Row 7 of A255107.

%H R. H. Hardin, <a href="/A255114/b255114.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/120)*n^5 + (5/12)*n^4 + (187/24)*n^3 + (7393/12)*n^2 + (20667/10)*n + 1143 for n>5.

%F Empirical g.f.: x*(6561 - 24517*x + 28659*x^2 - 1050*x^3 - 20126*x^4 + 11682*x^5 - 2967*x^6 + 3385*x^7 - 168*x^8 - 2466*x^9 + 1008*x^10) / (1 - x)^6. - _Colin Barker_, Jan 24 2018

%e Some solutions for n=4:

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

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

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

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

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

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

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

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

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

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

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

%Y Cf. A255107.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 14 2015