A249713 - OEIS

%I #8 Nov 10 2018 05:46:41

%S 72,1177,7056,27113,80360,200489,442144,888465,1659976,2924889,

%T 4910896,7918521,12336104,18656489,27495488,39612193,55931208,

%U 77566873,105849552,142354057,188930280,247736105,321272672,412422065,524487496,661236057

%N Number of length 7+3 0..n arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms.

%H R. H. Hardin, <a href="/A249713/b249713.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/70)*n^7 + (19/15)*n^6 + (178/15)*n^5 + 30*n^4 + (851/30)*n^3 + (56/15)*n^2 - (446/105)*n + 1.

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

%F G.f.: x*(72 + 601*x - 344*x^2 - 411*x^3 + 152*x^4 - 5*x^5 + 8*x^6 - x^7) / (1 - x)^8.

%F 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 (End)

%e Some solutions for n=5:

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

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

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

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

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

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

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

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

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

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

%Y Row 7 of A249707.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 04 2014