A200837 - OEIS

%I #10 Oct 16 2017 12:21:46

%S 400,2444,15128,93472,577660,3570086,22063924,136360286,842739040,

%T 5208328180,32188710564,198933910242,1229459024390,7598350081290,

%U 46959616234372,290221631449614,1793638920327662,11085116434803236

%N Number of 0..7 arrays x(0..n+1) of n+2 elements without any two consecutive increases or two consecutive decreases.

%C Column 7 of A200838.

%H R. H. Hardin, <a href="/A200837/b200837.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 8*a(n-1) -12*a(n-2) +6*a(n-3) -10*a(n-4) +12*a(n-5) -11*a(n-6) +11*a(n-7) -6*a(n-8) +3*a(n-9) -a(n-10).

%F Empirical g.f.: 2*x*(200 - 378*x + 188*x^2 - 312*x^3 + 378*x^4 - 329*x^5 + 338*x^6 - 183*x^7 + 92*x^8 - 32*x^9) / (1 - 8*x + 12*x^2 - 6*x^3 + 10*x^4 - 12*x^5 + 11*x^6 - 11*x^7 + 6*x^8 - 3*x^9 + x^10). - _Colin Barker_, Oct 16 2017

%e Some solutions for n=3

%e ..7....3....6....6....2....3....0....3....7....0....2....1....1....0....3....0

%e ..2....3....5....0....3....5....4....2....1....5....0....0....7....0....2....3

%e ..7....6....6....4....2....5....2....7....4....4....4....5....3....4....2....3

%e ..4....1....6....0....5....5....5....1....2....7....0....0....4....2....6....0

%e ..7....5....5....5....2....3....0....1....4....6....0....4....4....4....5....0

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 23 2011