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Number of n X nX44 0..2 arrays with rows unimodal and columns nondecreasing.
Column 4 of A224190.
Empirical: a(n) = (41/4032)*n^8 + (55/336)*n^7 + (179/160)*n^6 + (169/40)*n^5 + (615/64)*n^4 + (215/16)*n^3 + (56759/5040)*n^2 + (2173/420)*n + 1.
Conjectures from Colin Barker, Aug 29 2018: (Start)
G.f.: x*(46 + 134*x + 250*x^2 - 91*x^3 + 127*x^4 - 84*x^5 + 36*x^6 - 9*x^7 + x^8) / (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>9.
(End)
Some solutions for n=3:
Cf. A224190.
_R. H. Hardin_ _, Apr 01 2013
R. H. Hardin, <a href="/A224186/b224186.txt">Table of n, a(n) for n = 1..210</a>
allocated for R. H. Hardin
Number of nX4 0..2 arrays with rows unimodal and columns nondecreasing
46, 548, 3526, 15779, 55438, 163746, 424326, 992607, 2138488, 4305730, 8191976, 14853709, 25840868, 43366252, 70515252, 111501861, 171977322, 259398184, 383460946, 556610879, 794633026, 1117333790, 1549321930, 2120898195
1,1
Column 4 of A224190
Empirical: a(n) = (41/4032)*n^8 + (55/336)*n^7 + (179/160)*n^6 + (169/40)*n^5 + (615/64)*n^4 + (215/16)*n^3 + (56759/5040)*n^2 + (2173/420)*n + 1
Some solutions for n=3
..0..1..0..0....1..1..1..1....2..1..0..0....0..1..2..0....0..1..0..0
..1..1..0..0....1..1..1..1....2..1..1..0....0..2..2..0....0..1..1..0
..1..2..0..0....1..1..1..1....2..2..1..1....0..2..2..0....1..1..1..0
allocated
nonn
R. H. Hardin Apr 01 2013
