cp's OEIS Frontend

A255998 Number of length n+7 0..1 arrays with at most one downstep in every n consecutive neighbor pairs.

%I A255998 #7 Jan 26 2018 06:14:54
%S A255998 256,512,667,796,945,1134,1352,1584,1831,2094,2374,2672,2989,3326,
%T A255998 3684,4064,4467,4894,5346,5824,6329,6862,7424,8016,8639,9294,9982,
%U A255998 10704,11461,12254,13084,13952,14859,15806,16794,17824,18897,20014,21176,22384,23639
%N A255998 Number of length n+7 0..1 arrays with at most one downstep in every n consecutive neighbor pairs.
%C A255998 Row 7 of A255992.
%H A255998 R. H. Hardin, <a href="/A255998/b255998.txt">Table of n, a(n) for n = 1..210</a>
%F A255998 Empirical: a(n) = (1/6)*n^3 + (7/2)*n^2 + (454/3)*n + 64 for n>5.
%F A255998 Empirical g.f.: x*(256 - 512*x + 155*x^2 + 176*x^3 - 29*x^4 - 26*x^5 - 31*x^6 - 4*x^7 + 16*x^8) / (1 - x)^4. - _Colin Barker_, Jan 26 2018
%e A255998 Some solutions for n=4:
%e A255998 ..1....1....0....0....0....0....0....1....0....0....1....0....0....0....0....1
%e A255998 ..0....1....0....1....0....0....0....0....0....0....0....0....1....1....0....1
%e A255998 ..1....1....0....1....0....0....0....1....0....0....1....1....1....1....1....0
%e A255998 ..1....0....0....0....0....1....0....1....0....0....1....0....1....0....1....0
%e A255998 ..1....1....0....0....1....1....1....1....0....0....1....0....1....0....0....0
%e A255998 ..0....1....0....0....0....0....1....1....1....0....1....0....1....0....1....0
%e A255998 ..0....1....0....0....0....0....1....0....1....0....0....1....0....0....1....1
%e A255998 ..0....0....1....0....1....0....1....0....1....0....1....1....0....1....1....1
%e A255998 ..0....0....0....0....1....0....1....1....1....0....1....0....0....0....0....1
%e A255998 ..1....0....1....0....1....0....1....1....1....1....1....0....0....0....1....1
%e A255998 ..0....1....1....0....1....0....0....0....1....1....1....1....0....1....1....0
%Y A255998 Cf. A255992.
%K A255998 nonn
%O A255998 1,1
%A A255998 _R. H. Hardin_, Mar 13 2015