cp's OEIS Frontend

A229017 Number of arrays of median of three adjacent elements of some length 9 0..n array, with no adjacent equal elements in the latter.

%I A229017 #11 Sep 14 2018 11:59:37
%S A229017 2,193,2054,10735,38768,111311,273124,597477,1197190,2238005,3954490,
%T A229017 6668675,10811620,16948115,25804712,38301289,55586346,79076233,
%U A229017 110498510,151939639,205897208,275336887,363754316,475242125,614562286,787223997
%N A229017 Number of arrays of median of three adjacent elements of some length 9 0..n array, with no adjacent equal elements in the latter.
%H A229017 R. H. Hardin, <a href="/A229017/b229017.txt">Table of n, a(n) for n = 1..158</a>
%F A229017 Empirical: a(n) = (5/126)*n^7 + (233/180)*n^6 + (1073/180)*n^5 - (85/18)*n^4 - (89/36)*n^3 + (617/180)*n^2 - (177/70)*n + 1.
%F A229017 Conjectures from _Colin Barker_, Sep 14 2018: (Start)
%F A229017 G.f.: x*(2 + 177*x + 566*x^2 - 405*x^3 - 268*x^4 + 121*x^5 + 8*x^6 - x^7) / (1 - x)^8.
%F A229017 a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
%F A229017 (End)
%e A229017 Some solutions for n=4:
%e A229017 ..2....3....3....0....3....3....4....3....1....3....1....0....1....4....3....4
%e A229017 ..3....4....2....3....4....3....2....3....0....4....1....1....2....3....4....3
%e A229017 ..3....3....2....1....1....1....1....3....2....0....2....2....0....4....1....3
%e A229017 ..2....3....1....3....1....1....1....0....1....4....2....2....4....3....3....0
%e A229017 ..1....3....4....1....1....1....0....3....4....3....1....2....2....2....0....1
%e A229017 ..1....3....2....4....2....4....3....2....1....3....1....1....3....2....3....1
%e A229017 ..2....4....4....1....3....0....3....3....2....1....1....1....3....1....3....3
%Y A229017 Row 7 of A229012.
%K A229017 nonn
%O A229017 1,1
%A A229017 _R. H. Hardin_, Sep 10 2013