|
%I #8 Jan 24 2018 16:46:31
%S 729,1791,2907,4429,6582,9297,12662,16779,21765,27753,34893,43353,
%T 53320,65001,78624,94439,112719,133761,157887,185445,216810,252385,
%U 292602,337923,388841,445881,509601,580593,659484,746937,843652,950367,1067859
%N Number of length n+5 0..2 arrays with at most one downstep in every n consecutive neighbor pairs.
%C Row 5 of A255107.
%H R. H. Hardin, <a href="/A255112/b255112.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/120)*n^5 + (1/3)*n^4 + (115/24)*n^3 + (889/6)*n^2 + (3867/10)*n + 111 for n>3.
%F Empirical g.f.: x*(729 - 2583*x + 3096*x^2 - 728*x^3 - 1272*x^4 + 591*x^5 + 618*x^6 - 594*x^7 + 144*x^8) / (1 - x)^6. - _Colin Barker_, Jan 24 2018
%e Some solutions for n=4:
%e ..0....2....1....0....1....2....1....1....0....1....0....2....1....0....0....2
%e ..2....0....1....1....0....2....1....0....2....0....2....2....0....2....2....0
%e ..2....0....1....0....0....1....2....1....1....0....0....0....0....2....2....0
%e ..0....2....1....0....1....1....1....1....1....2....0....1....0....2....2....0
%e ..0....2....0....1....2....2....1....2....1....2....2....1....0....2....1....0
%e ..2....2....0....2....2....2....1....2....1....2....2....1....0....0....1....0
%e ..2....0....0....0....1....0....2....1....0....2....2....2....0....1....1....2
%e ..1....1....1....1....2....1....0....1....0....2....1....0....0....1....2....2
%e ..2....1....1....2....2....1....2....2....0....0....2....0....1....1....1....1
%Y Cf. A255107.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 14 2015
| 