A200882 - OEIS

%I #10 Oct 16 2017 09:59:31

%S 95,325,1121,3985,14288,50995,181336,644721,2294193,8166441,29066618,

%T 103444256,368138471,1310164527,4662787112,16594519920,59058487061,

%U 210183969235,748026706926,2662163892493,9474416502527,33718645047381

%N Number of 0..4 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors.

%C Column 4 of A200886.

%H R. H. Hardin, <a href="/A200882/b200882.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) -10*a(n-2) +20*a(n-3) -15*a(n-4) +21*a(n-5) -7*a(n-6) +8*a(n-7) -a(n-8) +a(n-9).

%F Empirical g.f.: x*(95 - 150*x + 446*x^2 - 270*x^3 + 498*x^4 - 135*x^5 + 196*x^6 - 20*x^7 + 25*x^8) / (1 - 5*x + 10*x^2 - 20*x^3 + 15*x^4 - 21*x^5 + 7*x^6 - 8*x^7 + x^8 - x^9). - _Colin Barker_, Oct 16 2017

%e Some solutions for n=3

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 23 2011