cp's OEIS Frontend

A258735 Number of length n+5 0..3 arrays with at most one downstep in every n consecutive neighbor pairs.

%I A258735 #7 Jan 26 2018 08:36:34
%S A258735 4096,11704,20955,35540,59188,92548,138196,199264,279560,383704,
%T A258735 517281,687012,900944,1168660,1501510,1912864,2418388,3036344,3787915,
%U A258735 4697556,5793372,7107524,8676664,10542400,12751792,15357880,18420245,22005604
%N A258735 Number of length n+5 0..3 arrays with at most one downstep in every n consecutive neighbor pairs.
%C A258735 Row 5 of A258730.
%H A258735 R. H. Hardin, <a href="/A258735/b258735.txt">Table of n, a(n) for n = 1..210</a>
%F A258735 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 A258735 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 A258735 Some solutions for n=4:
%e A258735 ..0....0....3....3....1....0....3....0....1....0....1....2....1....0....2....1
%e A258735 ..0....0....2....3....3....2....3....0....3....0....2....2....1....0....1....1
%e A258735 ..0....2....2....3....3....1....2....0....3....0....1....1....1....0....2....0
%e A258735 ..1....2....2....0....0....1....2....0....0....0....1....1....1....0....2....0
%e A258735 ..1....0....2....1....1....2....2....1....0....2....1....1....3....3....2....2
%e A258735 ..2....1....3....1....3....2....3....1....2....0....2....1....3....2....3....3
%e A258735 ..2....2....3....2....3....2....1....1....3....0....0....2....3....2....3....1
%e A258735 ..2....2....0....1....1....2....1....1....0....0....1....0....3....2....0....2
%e A258735 ..0....2....1....3....1....0....2....2....0....0....2....3....1....3....3....3
%Y A258735 Cf. A258730.
%K A258735 nonn
%O A258735 1,1
%A A258735 _R. H. Hardin_, Jun 08 2015