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A250893 Number of (n+1) X (3+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction. 1
403, 1325, 4388, 14196, 44525, 136509, 412006, 1231112, 3657629, 10837431, 32088956, 95066910, 281997715, 837788285, 2492972738, 7429400340, 22170161033, 66233321571, 198057333352, 592697831402, 1774742767583, 5316672917289 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = 12*a(n-1) - 60*a(n-2) + 162*a(n-3) - 255*a(n-4) + 234*a(n-5) - 116*a(n-6) + 24*a(n-7) for n>9.
Conjectures from Colin Barker, Nov 23 2018: (Start)
G.f.: x*(403 - 3511*x + 12668*x^2 - 24246*x^3 + 25568*x^4 - 13314*x^5 + 1284*x^6 + 1746*x^7 - 594*x^8) / ((1 - x)^3*(1 - 2*x)^3*(1 - 3*x)).
a(n) = (-8*(179+223*2^n-25*3^(3+n)) + (1104-845*2^n)*n + (32+375*2^n)*n^2) / 32 for n>2.
(End)
EXAMPLE
Some solutions for n=4:
..1..2..1..1....1..1..0..0....2..1..0..1....2..2..1..0....2..0..1..0
..0..1..0..0....1..2..1..1....1..2..1..2....2..2..2..1....2..0..1..2
..1..2..1..2....1..2..1..1....1..2..1..2....1..1..1..0....2..0..1..2
..1..2..1..2....0..1..0..0....1..2..1..2....1..1..1..1....2..0..1..2
..0..1..0..1....0..2..2..2....1..2..1..2....1..1..1..2....2..0..1..2
CROSSREFS
Column 3 of A250898.
Sequence in context: A325151 A213605 A083815 * A261857 A165808 A283662
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 28 2014
STATUS
approved

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Last modified December 10 14:46 EST 2023. Contains 367710 sequences. (Running on oeis4.)