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Number of length n+5 0..3 arrays with at most one downstep in every n consecutive neighbor pairs.
1

%I #7 Jan 26 2018 08:36:34

%S 4096,11704,20955,35540,59188,92548,138196,199264,279560,383704,

%T 517281,687012,900944,1168660,1501510,1912864,2418388,3036344,3787915,

%U 4697556,5793372,7107524,8676664,10542400,12751792,15357880,18420245,22005604

%N Number of length n+5 0..3 arrays with at most one downstep in every n consecutive neighbor pairs.

%C Row 5 of A258730.

%H R. H. Hardin, <a href="/A258735/b258735.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/5040)*n^7 + (1/80)*n^6 + (241/720)*n^5 + (229/48)*n^4 + (15569/90)*n^3 + (58693/60)*n^2 + (175526/105)*n + 512 for n>3.

%F Empirical g.f.: x*(4096 - 21064*x + 42011*x^2 - 33764*x^3 - 7096*x^4 + 30588*x^5 - 9050*x^6- 20224*x^7 + 22372*x^8 - 9344*x^9 + 1476*x^10) / (1 - x)^8. - _Colin Barker_, Jan 26 2018

%e Some solutions for n=4:

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

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

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

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

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

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

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

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

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

%Y Cf. A258730.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jun 08 2015