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Number of (n+1)) X( (3+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

Column 3 of A250729

Empirical: a(n) = 4*a(n-1) -) - 5*a(n-2) +) + 5*a(n-4) -) - 4*a(n-5) +) + a(n-6)).

Empirical for n mod 2 = 0: a(n) = (1/6)*n^4 + (4/3)*n^3 + (91/12)*n^2 + (74/3)*n + 17.

Empirical for n mod 2 = 1: a(n) = (1/6)*n^4 + (4/3)*n^3 + (91/12)*n^2 + (74/3)*n + (65/4)).

Empirical g.f.: x*(50 - 90*x + 18*x^2 + 83*x^3 - 70*x^4 + 17*x^5) / ((1 - x)^5*(1 + x)). - Colin Barker, Nov 16 2018

Some solutions for n=4:

Column 3 of A250729.

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R. H. Hardin, <a href="/A250724/b250724.txt">Table of n, a(n) for n = 1..210</a>

allocated for R. H. Hardin

Number of (n+1)X(3+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction

50, 110, 208, 365, 600, 942, 1418, 2065, 2918, 4022, 5420, 7165, 9308, 11910, 15030, 18737, 23098, 28190, 34088, 40877, 48640, 57470, 67458, 78705, 91310, 105382, 121028, 138365, 157508, 178582, 201710, 227025, 254658, 284750, 317440, 352877

1,1

Column 3 of A250729

Empirical: a(n) = 4*a(n-1) -5*a(n-2) +5*a(n-4) -4*a(n-5) +a(n-6)

Empirical for n mod 2 = 0: a(n) = (1/6)*n^4 + (4/3)*n^3 + (91/12)*n^2 + (74/3)*n + 17

Empirical for n mod 2 = 1: a(n) = (1/6)*n^4 + (4/3)*n^3 + (91/12)*n^2 + (74/3)*n + (65/4)

Some solutions for n=4

..0..0..0..1....0..0..0..1....0..0..0..0....0..0..0..0....0..0..0..0

..0..0..0..1....0..0..1..1....0..0..0..0....0..1..1..1....0..0..0..1

..0..1..1..1....0..0..1..1....0..0..0..1....0..1..1..1....0..1..1..1

..1..1..1..1....0..0..1..1....0..0..0..1....0..1..1..1....1..1..1..1

..1..1..1..1....1..0..1..1....0..0..0..1....1..1..1..1....1..1..1..1

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nonn

R. H. Hardin, Nov 27 2014

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