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A253517
Number of (n+1) X (1+1) 0..2 arrays with every 2 X 2 subblock diagonal minimum minus antidiagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal maximum nondecreasing vertically.
2
81, 470, 2180, 9623, 42669, 192393, 876277, 4010555, 18395493, 84458827, 387945181, 1782308819, 8189083701, 37627550715, 172896033837, 794452690915, 3650504500581, 16774075855627, 77076986789213, 354169411790451
OFFSET
1,1
COMMENTS
Column 1 of A253524.
LINKS
FORMULA
Empirical: a(n) = 8*a(n-1) - 15*a(n-2) - 12*a(n-3) + 44*a(n-4) - 8*a(n-5) - 16*a(n-6) for n>13.
Empirical g.f.: x*(81 - 178*x - 365*x^2 + 205*x^3 + 461*x^4 + 1514*x^5 + 1780*x^6 - 190*x^7 - 1648*x^8 - 1440*x^9 - 720*x^10 - 224*x^11 - 32*x^12) / ((1 - x)*(1 - 2*x)*(1 - 5*x - 2*x^2 + 16*x^3 + 8*x^4)). - Colin Barker, Mar 20 2018
EXAMPLE
Some solutions for n=4:
..2..1....2..2....0..1....0..0....1..1....0..2....2..2....1..1....1..2....2..0
..2..1....2..0....1..1....2..2....2..1....1..0....2..1....2..2....0..1....2..2
..2..0....2..1....1..1....0..0....2..0....2..1....2..0....2..2....0..0....2..2
..1..1....1..1....0..1....0..0....1..0....0..1....2..2....0..2....1..0....2..1
..1..2....1..2....1..2....1..2....1..2....1..2....0..1....1..2....2..0....2..2
CROSSREFS
Cf. A253524.
Sequence in context: A334036 A253524 A254422 * A237683 A236640 A236780
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 03 2015
STATUS
approved