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A253752
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Number of (4+1) X (n+1) 0..2 arrays with every 2 X 2 subblock ne-sw antidiagonal difference nondecreasing horizontally and nw+se diagonal sum nondecreasing vertically.
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2
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7803, 75959, 382973, 1143174, 2351928, 4249381, 7348144, 11783014, 17227486, 24218260, 33845194, 46241656, 60632621, 78042368, 100341383, 127587830, 158431665, 194599303, 238993938, 291534619, 350130482, 417457176, 497739626
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +4*a(n-4) -12*a(n-5) +12*a(n-6) -4*a(n-7) -6*a(n-8) +18*a(n-9) -18*a(n-10) +6*a(n-11) +4*a(n-12) -12*a(n-13) +12*a(n-14) -4*a(n-15) -a(n-16) +3*a(n-17) -3*a(n-18) +a(n-19) for n>27.
Empirical for n mod 4 = 0: a(n) = (4873/23040)*n^6 + (241919/15360)*n^5 + (3034139/4608)*n^4 + (4726559/384)*n^3 + (7406437/90)*n^2 - (15218987/30)*n + 1005182 for n>8.
Empirical for n mod 4 = 1: a(n) = (4873/23040)*n^6 + (241919/15360)*n^5 + (3034139/4608)*n^4 + (18843205/1536)*n^3 + (1878126757/23040)*n^2 - (2674526163/5120)*n + (522413747/512) for n>8.
Empirical for n mod 4 = 2: a(n) = (4873/23040)*n^6 + (241919/15360)*n^5 + (3034139/4608)*n^4 + (146755/12)*n^3 + (14433929/180)*n^2 - (525506959/960)*n + (34331513/32) for n>8.
Empirical for n mod 4 = 3: a(n) = (4873/23040)*n^6 + (241919/15360)*n^5 + (3034139/4608)*n^4 + (18844129/1536)*n^3 + (1862199637/23040)*n^2 - (2736248123/5120)*n + (544432283/512) for n>8.
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EXAMPLE
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Some solutions for n=2
..2..0..0....0..0..2....1..0..1....0..1..2....0..0..2....1..0..0....1..0..0
..1..0..0....0..0..0....2..0..2....2..1..0....0..0..1....1..0..0....1..0..2
..1..1..1....2..0..0....1..0..2....2..1..2....0..0..1....2..0..1....2..1..2
..2..1..1....2..0..1....2..1..2....1..1..2....2..2..1....2..1..1....2..1..2
..2..0..1....2..2..1....0..1..2....1..2..2....2..0..0....2..2..0....1..1..2
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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