cp's OEIS Frontend

A229016 Number of arrays of median of three adjacent elements of some length 8 0..n array, with no adjacent equal elements in the latter.

%I A229016 #11 Sep 14 2018 11:57:20
%S A229016 2,105,830,3527,10860,27379,60180,119653,220318,381749,629586,996635,
%T A229016 1524056,2262639,3274168,4632873,6426970,8760289,11753990,15548367,
%U A229016 20304740,26207435,33465852,42316621,53025846,65891437,81245530,99456995
%N A229016 Number of arrays of median of three adjacent elements of some length 8 0..n array, with no adjacent equal elements in the latter.
%H A229016 R. H. Hardin, <a href="/A229016/b229016.txt">Table of n, a(n) for n = 1..178</a>
%F A229016 Empirical: a(n) = (11/90)*n^6 + (11/5)*n^5 + (167/36)*n^4 - (43/6)*n^3 + (583/180)*n^2 - (61/30)*n + 1.
%F A229016 Conjectures from _Colin Barker_, Sep 14 2018: (Start)
%F A229016 G.f.: x*(2 + 91*x + 137*x^2 - 148*x^3 - 4*x^4 + 9*x^5 + x^6) / (1 - x)^7.
%F A229016 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F A229016 (End)
%e A229016 Some solutions for n=4:
%e A229016 ..3....2....3....1....1....0....1....1....1....0....2....4....3....1....1....1
%e A229016 ..3....2....3....3....1....1....1....0....2....1....4....2....0....3....2....1
%e A229016 ..4....0....2....3....1....3....3....3....2....2....2....2....4....3....2....0
%e A229016 ..1....4....3....3....1....3....0....3....2....2....4....1....2....3....1....1
%e A229016 ..3....0....3....4....0....4....3....3....2....4....1....2....2....1....0....0
%e A229016 ..0....1....3....0....2....2....3....1....0....3....3....1....1....3....1....4
%Y A229016 Row 6 of A229012.
%K A229016 nonn
%O A229016 1,1
%A A229016 _R. H. Hardin_, Sep 10 2013