A258736 - OEIS

%I #7 Jan 26 2018 08:33:01

%S 16384,43681,68120,98676,149960,228081,331584,465580,635992,849708,

%T 1114752,1440474,1837760,2319263,2899656,3595908,4427584,5417170,

%U 6590424,7976754,9609624,11526989,13771760,16392300,19442952,22984600,27085264

%N Number of length n+6 0..3 arrays with at most one downstep in every n consecutive neighbor pairs.

%C Row 6 of A258730.

%H R. H. Hardin, <a href="/A258736/b258736.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/5040)*n^7 + (1/72)*n^6 + (149/360)*n^5 + (239/36)*n^4 + (297247/720)*n^3 + (187297/72)*n^2 + (178036/35)*n + 2212 for n>4.

%F Empirical g.f.: x*(16384 - 87391*x + 177424*x^2 - 140720*x^3 - 31344*x^4 + 116775*x^5 - 39024*x^6 - 13988*x^7 - 31192*x^8 + 58867*x^9 - 31680*x^10 + 5890*x^11) / (1 - x)^8. - _Colin Barker_, Jan 26 2018

%e Some solutions for n=4:

%e ..2....1....1....2....0....0....2....1....3....0....2....1....0....3....0....0

%e ..2....0....1....0....0....0....0....1....3....1....1....1....2....3....0....0

%e ..0....1....2....0....2....2....0....0....2....0....1....2....3....0....2....3

%e ..0....1....0....0....2....2....0....1....2....0....3....0....3....0....2....0

%e ..2....1....0....0....2....0....0....2....2....3....3....2....1....0....0....0

%e ..2....2....0....1....2....0....2....2....2....3....1....2....1....0....0....1

%e ..3....3....2....2....2....0....0....3....0....0....1....2....1....1....0....3

%e ..1....3....1....2....0....0....1....3....2....0....1....0....2....3....1....3

%e ..3....3....1....3....2....1....2....1....2....3....3....0....3....1....2....0

%e ..3....2....1....0....3....0....2....1....3....3....1....0....2....1....3....0

%Y Cf. A258730.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jun 08 2015