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Number of arrays of median of three adjacent elements of some length n+2 0..3 array, with no adjacent equal elements in the latter.
1

%I #8 Sep 13 2013 20:11:56

%S 4,14,46,130,332,830,2054,5108,12790,32146,80942,203898,513498,

%T 1292934,3254868,8193210,20623908,51914372,130680214,328953874,

%U 828059138,2084434524,5247046924,13208134738,33248182980,83693989466,210678694852

%N Number of arrays of median of three adjacent elements of some length n+2 0..3 array, with no adjacent equal elements in the latter.

%C Column 3 of A229012.

%H R. H. Hardin, <a href="/A229007/b229007.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) -5*a(n-3) +2*a(n-4) +11*a(n-5) -11*a(n-6) -2*a(n-7) +19*a(n-8) -8*a(n-9) -13*a(n-10) +28*a(n-11) -18*a(n-12) +a(n-13) +26*a(n-14) -24*a(n-15) +9*a(n-16) +15*a(n-17) -21*a(n-18) +13*a(n-19) +5*a(n-20) -12*a(n-21) +19*a(n-22) -9*a(n-23) -a(n-24) +4*a(n-25) -4*a(n-26) +2*a(n-27).

%e Some solutions for n=4

%e ..2....2....2....1....3....3....1....2....2....3....2....1....2....2....2....1

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 10 2013