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 A205065 Number of (n+1) X 2 0..1 arrays with the number of rightwards and downwards edge increases in each 2 X 2 subblock differing from the number in all its horizontal and vertical neighbors. 1

%I #10 Jun 10 2018 17:56:24

%S 16,40,98,238,584,1432,3516,8622,21158,51894,127322,312310,766198,

%T 1879520,4610912,11311058,27748262,68070236,166988412,409647388,

%U 1004934200,2465259322,6047686542,14835930358,36394946602,89282603930

%N Number of (n+1) X 2 0..1 arrays with the number of rightwards and downwards edge increases in each 2 X 2 subblock differing from the number in all its horizontal and vertical neighbors.

%C Column 1 of A205072.

%H R. H. Hardin, <a href="/A205065/b205065.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: 2*x*(8 + 20*x + 9*x^2 + 3*x^3 + 7*x^4 - 9*x^5 + 4*x^6 + 11*x^7 - 4*x^8 + x^9) / (1 - 5*x^2 - 2*x^3 - 4*x^5 + 3*x^6 - 4*x^8 + 2*x^9). - _Colin Barker_, Jun 10 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Cf. A205072.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 21 2012

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Last modified June 4 23:50 EDT 2023. Contains 363130 sequences. (Running on oeis4.)