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Number of nX4 n X 4 0..1 arrays with rows and columns unimodal and antidiagonals nondecreasing.

Column 4 of A223777.

Empirical: a(n) = (1/40320)*n^8 + (1/3360)*n^7 + (19/2880)*n^6 + (7/120)*n^5 + (2447/5760)*n^4 + (259/160)*n^3 + (126691/10080)*n^2 - (12329/840)*n + 13 for n>1.

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

G.f.: x*(11 - 43*x + 72*x^2 - 67*x^3 + 53*x^4 - 50*x^5 + 34*x^6 - 6*x^7 - 5*x^8 + 2*x^9) / (1 - x)^9.

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>10.

(End)

Some solutions for n=3:

Cf. A223777.

R. H. Hardin , Mar 27 2013

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R. H. Hardin, <a href="/A223773/b223773.txt">Table of n, a(n) for n = 1..210</a>

allocated for R. H. Hardin

Number of nX4 0..1 arrays with rows and columns unimodal and antidiagonals nondecreasing

11, 56, 180, 461, 1040, 2164, 4246, 7950, 14308, 24877, 41945, 68796, 110045, 172055, 263449, 395731, 584031, 847990, 1212802, 1710431, 2381022, 3274526, 4452560, 5990524, 7979998, 10531443, 13777231, 17875030, 23011571, 29406825, 37318619

1,1

Column 4 of A223777

Empirical: a(n) = (1/40320)*n^8 + (1/3360)*n^7 + (19/2880)*n^6 + (7/120)*n^5 + (2447/5760)*n^4 + (259/160)*n^3 + (126691/10080)*n^2 - (12329/840)*n + 13 for n>1

Some solutions for n=3

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

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

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

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nonn

R. H. Hardin Mar 27 2013

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