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Number of (1+1)) X( (n+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.

Row 1 of A250898

Empirical: a(n) = 9*a(n-1) -) - 31*a(n-2) +) + 51*a(n-3) -) - 40*a(n-4) +) + 12*a(n-5)).

Conjectures from Colin Barker, Nov 23 2018: (Start)

G.f.: x*(37 - 206*x + 407*x^2 - 348*x^3 + 108*x^4) / ((1 - x)^2*(1 - 2*x)^2*(1 - 3*x)).

a(n) = (7 - 2^(4+n) + 3^(3+n) + (2+2^(3+n))*n) / 2.

(End)

Some solutions for n=4:

Row 1 of A250898.

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R. H. Hardin, <a href="/A250899/b250899.txt">Table of n, a(n) for n = 1..210</a>

allocated for R. H. Hardin

Number of (1+1)X(n+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

37, 127, 403, 1229, 3673, 10875, 32095, 94729, 280069, 829943, 2465227, 7338309, 21883825, 65356531, 195414199, 584800769, 1751256541, 5246953839, 15726181411, 47147086909, 141374151817, 423979849067, 1271637557263, 3814275137529

1,1

Row 1 of A250898

Empirical: a(n) = 9*a(n-1) -31*a(n-2) +51*a(n-3) -40*a(n-4) +12*a(n-5)

Some solutions for n=4

..1..1..1..0..0....0..2..2..1..0....2..1..1..2..1....2..2..1..2..0

..2..2..2..1..1....0..2..2..1..2....2..1..1..2..1....2..2..1..2..1

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nonn

R. H. Hardin, Nov 28 2014

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