A263595 - OEIS

%I #4 Oct 22 2015 12:43:20

%S 1,2,6,16,52,208,800,2900,10960,40792,148288,544600,2000084,7312332,

%T 26795812,98234356,359845004,1319030780,4834945864,17718152672,

%U 64944710636,238041386504,872396576888,3197533964256,11719620057508

%N Number of length n arrays of permutations of 0..n-1 with each element moved by -6 to 6 places and the median of every three consecutive elements nondecreasing.

%C Column 6 of A263597.

%H R. H. Hardin, <a href="/A263595/b263595.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) +a(n-2) +27*a(n-3) +11*a(n-4) +19*a(n-5) -17*a(n-6) +55*a(n-7) +207*a(n-8) +399*a(n-9) +842*a(n-10) +4810*a(n-11) +7064*a(n-12) -5048*a(n-13) -11662*a(n-14) +10885*a(n-15) -23133*a(n-16) -24495*a(n-17) +19889*a(n-18) -61624*a(n-19) -96905*a(n-20) -82792*a(n-21) -121206*a(n-22) -43903*a(n-23) -440813*a(n-24) -321679*a(n-25) +36248*a(n-26) -1481424*a(n-27) -184710*a(n-28) -147760*a(n-29) -954886*a(n-30) -1689620*a(n-31) +910782*a(n-32) -876748*a(n-33) -1449360*a(n-34) +1330892*a(n-35) +2445848*a(n-36) -1219064*a(n-37) +1399100*a(n-38) +2785232*a(n-39) +286256*a(n-40) +544140*a(n-41) +1489220*a(n-42) -40800*a(n-43) -524376*a(n-44) -119768*a(n-45) -395576*a(n-46) +110160*a(n-47) +418424*a(n-48) +649656*a(n-49) -332096*a(n-50) +215424*a(n-51) +84720*a(n-52) -2800*a(n-53) +293600*a(n-54) -3744*a(n-55) +128256*a(n-56) +40704*a(n-57) +10944*a(n-58) +11712*a(n-59) +2176*a(n-60) +9472*a(n-61) -1664*a(n-62) +3840*a(n-63) -2816*a(n-64) -256*a(n-65) -512*a(n-67)

%e Some solutions for n=6

%e ..2....4....1....1....5....0....0....4....1....0....2....0....1....1....0....1

%e ..3....0....2....0....0....2....2....0....2....2....5....1....0....0....3....0

%e ..0....1....0....2....1....3....1....1....5....4....0....3....2....5....1....3

%e ..4....3....4....5....3....4....4....5....3....1....3....2....5....2....4....2

%e ..5....2....5....4....2....1....5....3....0....3....4....4....3....3....5....4

%e ..1....5....3....3....4....5....3....2....4....5....1....5....4....4....2....5

%Y Cf. A263597.

%K nonn

%O 1,2

%A _R. H. Hardin_, Oct 22 2015