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Number of (n+1) X (2+1) 0..1 arrays with every 2X2 2 X 2 subblock ne-sw antidiagonal difference nondecreasing horizontally and nw+se diagonal sum nondecreasing vertically.

Column 2 of A258554

Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + a(n-3) + 3*a(n-4) - 4*a(n-5) + 2*a(n-6) + 2*a(n-7) - 3*a(n-8) + a(n-9) for n>11.

Empirical g.f.: x*(44 - 64*x + 68*x^2 - 16*x^3 - 43*x^4 + 18*x^5 + 12*x^6 - 12*x^7 - 2*x^8 + 6*x^9 - x^10) / ((1 - x)^3*(1 - x - x^2 - x^4 + x^6)). - Colin Barker, Dec 21 2018

Some solutions for n=4:

Cf. A258554

Column 2 of A258554.

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R. H. Hardin, <a href="/A258548/b258548.txt">Table of n, a(n) for n = 1..210</a>

allocated for R. H. Hardin

Number of (n+1)X(2+1) 0..1 arrays with every 2X2 subblock ne-sw antidiagonal difference nondecreasing horizontally and nw+se diagonal sum nondecreasing vertically

44, 112, 296, 652, 1329, 2530, 4667, 8419, 14932, 26184, 45561, 78903, 136170, 234461, 403075, 692272, 1188185, 2038466, 3496239, 5995441, 10279967, 17625041, 30216773, 51802782, 88807568, 152244537, 260993810, 447421309, 767011467

1,1

Column 2 of A258554

Empirical: a(n) = 4*a(n-1) -5*a(n-2) +a(n-3) +3*a(n-4) -4*a(n-5) +2*a(n-6) +2*a(n-7) -3*a(n-8) +a(n-9) for n>11

Some solutions for n=4

..0..0..1....1..1..1....0..0..0....0..0..1....0..0..1....0..0..0....1..0..0

..0..0..0....0..0..0....1..1..1....1..0..1....1..0..1....0..0..1....0..0..0

..1..0..1....1..1..1....0..0..0....1..0..1....1..0..1....0..0..1....1..1..0

..1..0..1....1..0..0....1..1..1....0..0..1....1..0..1....1..1..1....1..0..0

..0..0..1....1..1..1....1..0..1....1..1..1....0..1..1....1..1..0....1..1..1

Cf. A258554

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nonn

R. H. Hardin, Jun 03 2015

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