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A253391
Number of (n+1) X (2+1) 0..1 arrays with every 2 X 2 subblock antidiagonal maximum minus diagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal minimum nondecreasing vertically.
1
44, 102, 143, 197, 250, 320, 391, 477, 564, 666, 769, 887, 1006, 1140, 1275, 1425, 1576, 1742, 1909, 2091, 2274, 2472, 2671, 2885, 3100, 3330, 3561, 3807, 4054, 4316, 4579, 4857, 5136, 5430, 5725, 6035, 6346, 6672, 6999, 7341, 7684, 8042, 8401, 8775, 9150
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>8.
Empirical for n mod 2 = 0: a(n) = 4*n^2 + (45/2)*n + 41 for n>4.
Empirical for n mod 2 = 1: a(n) = 4*n^2 + (45/2)*n + (75/2) for n>4.
Empirical g.f.: x*(44 + 14*x - 61*x^2 - x^3 + 16*x^4 + 4*x^5 + 2*x^6 - 2*x^7) / ((1 - x)^3*(1 + x)). - Colin Barker, Dec 11 2018
EXAMPLE
Some solutions for n=4:
..1..1..1....1..1..1....0..1..1....1..1..1....1..1..1....0..1..0....1..0..1
..1..1..1....1..1..0....0..0..0....1..1..0....0..1..0....1..1..0....0..0..0
..1..1..0....1..1..1....0..0..1....0..1..0....0..1..0....1..1..0....0..1..0
..0..1..0....0..0..0....0..0..1....0..1..0....0..1..0....1..1..1....0..1..0
..0..1..0....0..1..1....0..0..1....0..1..0....0..1..0....1..0..0....0..1..0
CROSSREFS
Column 2 of A253397.
Sequence in context: A129289 A039527 A375390 * A050944 A332590 A187933
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 31 2014
STATUS
approved