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Number of n X n nonnegative integer arrays with upper left entry 0, lower right entry n - 5, every value within 4 of its king-move distance from the upper left, and every value increasing by 0 or 1 with every step right, diagonally southeast, or down.
0

%I #17 Sep 05 2023 16:56:30

%S 0,0,0,0,1,251,35176,4105312,466029138,54944041476,6886218018445,

%T 920364154307990,130498580283240363,19482086451147555715,

%U 3039784702880850466554,492560752706827973431360,82451674043232981553367317,14196926753609833253834234271

%N Number of n X n nonnegative integer arrays with upper left entry 0, lower right entry n - 5, every value within 4 of its king-move distance from the upper left, and every value increasing by 0 or 1 with every step right, diagonally southeast, or down.

%H Robert Dougherty-Bliss and Manuel Kauers, <a href="https://arxiv.org/abs/2309.00487">Hardinian Arrays</a>, arXiv 2309.00487 [math.CO], 2023.

%F Conjecture: a(n) ~ (2^2 / (3^16 * Pi^2)) * 256^n / n^6.

%e Example for n = 7:

%e 0011112

%e 0111222

%e 0111222

%e 0112222

%e 0112222

%e 1111222

%e 2222222

%Y Cf. A253026, A253217, A252998.

%K nonn

%O 1,6

%A _Robert Dougherty-Bliss_, Sep 04 2023