A249885 - OEIS

%I #8 Nov 10 2018 05:46:38

%S 35,1365,18390,136010,684585,2644815,8435180,23274900,57355695,

%T 129095945,269791170,530015070,988165685,1761591555,3020773080,

%U 5007074600,8054623035,12616909245,19298748590,28894277490,42431703105,61225563575

%N Number of length 2+6 0..n arrays with no seven consecutive terms having the maximum of any three terms equal to the minimum of the remaining four terms.

%H R. H. Hardin, <a href="/A249885/b249885.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = n^8 + (16/7)*n^7 + (16/3)*n^6 + 8*n^5 + (59/6)*n^4 + 7*n^3 + (4/3)*n^2 + (3/14)*n.

%F Conjectures from _Colin Barker_, Nov 10 2018: (Start)

%F G.f.: 5*x*(7 + 210*x + 1473*x^2 + 3340*x^3 + 2457*x^4 + 546*x^5 + 31*x^6) / (1 - x)^9.

%F a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.

%F (End)

%e Some solutions for n=4:

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

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

%e ..3....2....3....4....2....4....4....4....3....0....3....4....0....0....2....4

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

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

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

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

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

%Y Row 2 of A249883.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 07 2014