A219737 - OEIS

%I #10 Mar 12 2018 09:39:55

%S 7,28,126,524,2229,9425,39905,168925,715072,3027049,12813931,54243509,

%T 229621433,972024617,4114736810,17418344167,73734658344,312130693269,

%U 1321299533915,5593273893746,23677229915913,100229530526756

%N Unmatched value maps: number of n X 4 binary arrays indicating the locations of corresponding elements not equal to any horizontal, vertical or antidiagonal neighbor in a random 0..1 n X 4 array.

%C Column 4 of A219741.

%H R. H. Hardin, <a href="/A219737/b219737.txt">Table of n, a(n) for n = 1..130</a>

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

%F Zeilberger's Maple code (see links in A228285) would give a proof that this recurrence is correct. - _N. J. A. Sloane_, Aug 22 2013

%F G.f.: x*(1 + x)*(7 + 14*x + 14*x^2 - x^3 - 2*x^4 - 2*x^5 + 3*x^6 - x^7) / (1 - x - 10*x^2 - 15*x^3 - 4*x^4 + 6*x^5 + x^6 - 3*x^7 + x^8). - _Colin Barker_, Mar 12 2018

%e Some solutions for n=3:

%e ..0..1..0..1....0..0..1..0....0..0..0..1....1..0..1..0....1..0..0..0

%e ..0..0..0..0....1..0..0..0....1..0..0..0....0..0..0..0....0..0..0..0

%e ..1..0..0..0....0..1..0..1....0..1..0..0....0..1..0..1....1..0..0..0

%Y Cf. A219741.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 26 2012