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A259214 Number of (n+1)X(n+1) 0..1 arrays with each 2X2 subblock having clockwise pattern 0000 0011 or 0101.

%I A259214 #8 Jun 02 2025 11:49:21
%S A259214 7,23,66,183,487,1278,3319,8591,22210,57455,148815,386046,1002991,
%T A259214 2609559,6797794
%N A259214 Number of (n+1)X(n+1) 0..1 arrays with each 2X2 subblock having clockwise pattern 0000 0011 or 0101.
%C A259214 Diagonal of A259222
%F A259214 Empirical: a(n) = 6*a(n-1) -10*a(n-2) -2*a(n-3) +16*a(n-4) -6*a(n-5) -5*a(n-6) +2*a(n-7)
%F A259214 Empirical g.f:  -x*(7-19*x-2*x^2+31*x^3-17*x^4-8*x^5+4*x^6)/(x-1)/(2*x-1)/(1+x)/(x^2-3*x+1)/(x^2+x-1) . - _R. J. Mathar_, Nov 09 2018
%F A259214 Empirical: a(n) = 18*A001906(n+1)/5 -7*A001906(n)/5 +2 + 4*2^n - 4*A000045(n+3)+2*(-1)^n /5. - _R. J. Mathar_, Nov 09 2018
%e A259214 Some solutions for n=4
%e A259214 ..0..0..0..0..1....0..1..1..0..1....1..1..1..1..1....1..0..1..0..0
%e A259214 ..0..0..0..0..1....1..0..0..1..0....0..0..0..0..0....0..1..0..1..1
%e A259214 ..0..0..0..0..1....0..1..1..0..1....0..0..0..0..0....1..0..1..0..0
%e A259214 ..0..0..0..0..1....1..0..0..1..0....1..1..1..1..1....1..0..1..0..0
%e A259214 ..0..0..0..0..1....1..0..0..1..0....0..0..0..0..0....0..1..0..1..1
%Y A259214 Cf. A259222
%K A259214 nonn
%O A259214 1,1
%A A259214 _R. H. Hardin_, Jun 21 2015