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A184073
Number of (n+1) X 2 0..2 arrays with rows and columns in nondecreasing order and with no 2 X 2 subblock sum differing from a horizontal or vertical neighbor subblock sum by more than one.
1
29, 58, 150, 335, 728, 1499, 2968, 5645, 10331, 18242, 31173, 51709, 83492, 131554, 202727, 306142, 453830, 661439, 949082, 1342332, 1873381, 2582381, 3518986, 4744115, 6331957, 8372240, 10972787, 14262383, 18393978, 23548252, 29937569
OFFSET
1,1
COMMENTS
Column 1 of A184081.
LINKS
FORMULA
Conjectures from Colin Barker, Apr 12 2018: (Start)
G.f.: x*(29 - 203*x + 672*x^2 - 1363*x^3 + 1895*x^4 - 1939*x^5 + 1573*x^6 - 1117*x^7 + 749*x^8 - 450*x^9 + 209*x^10 - 65*x^11 + 12*x^12 - x^13) / (1 - x)^9.
a(n) = (1290240 - 1768560*n + 1559788*n^2 - 343756*n^3 + 72569*n^4 - 4480*n^5 + 602*n^6 - 4*n^7 + n^8) / 40320 for n>5.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>14.
(End)
EXAMPLE
Some solutions for 3 X 2:
..0..0....0..1....0..2....0..2....0..0....0..2....0..2....0..1....0..1....0..1
..0..1....0..2....1..0....1..1....0..2....2..0....2..0....0..1....1..1....0..1
..0..1....1..0....2..0....2..0....1..0....2..1....2..0....0..2....1..1....1..1
...
...1.......3.......3.......4.......2.......4.......4.......2.......3.......2...
...2.......3.......3.......4.......3.......5.......4.......3.......4.......3...
CROSSREFS
Cf. A184081.
Sequence in context: A249079 A004942 A033904 * A080170 A078848 A055784
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 09 2011
STATUS
approved