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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 1 of A184081.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..200

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

Adjacent sequences:  A184070 A184071 A184072 * A184074 A184075 A184076

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jan 09 2011

STATUS

approved

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Last modified January 23 01:37 EST 2021. Contains 340384 sequences. (Running on oeis4.)