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A253489 Number of (n+1) X (2+1) 0..2 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally, vertically and ne-to-sw antidiagonally. 1

%I

%S 414,1377,2640,4720,9654,22236,55362,145428,397002,1114476,3192402,

%T 9277188,27233562,80506716,239134242,712632948,2128361322,6366010956,

%U 19059888882,57103380708,171157572282,513167579196,1538892464322

%N Number of (n+1) X (2+1) 0..2 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally, vertically and ne-to-sw antidiagonally.

%H R. H. Hardin, <a href="/A253489/b253489.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) for n>8.

%F Empirical: a(n) = 49*3^(n-1) + 291*2^(n-1) + 1017 for n>5.

%F Empirical g.f.: x*(414 - 1107*x - 1068*x^2 + 1543*x^3 + 2112*x^4 + 392*x^5 - 180*x^6 - 72*x^7) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - _Colin Barker_, Dec 15 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 2 of A253495.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 02 2015

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Last modified October 16 20:23 EDT 2019. Contains 328103 sequences. (Running on oeis4.)