A229775 Number of 3 X 3 0..n arrays with rows in lexicographically nondecreasing order and columns in nonincreasing order.

20, 322, 3232, 21331, 103222, 397460, 1287672, 3647349, 9281272, 21642038, 46934680, 95749927, 185397226, 343142248, 610590224, 1049496105, 1749325212, 2836933738, 4488787184, 6946186555, 10534026910, 15683670652, 22960578760

Offset: 1

Author

R. H. Hardin, Sep 29 2013

Keywords

• nonn

Examples

			Some solutions for n=3:
..1..0..0....1..1..0....1..0..0....1..1..1....1..1..0....1..0..0....2..0..0
..1..2..0....1..1..0....1..2..0....2..1..0....2..1..2....1..3..3....2..0..0
..3..3..0....3..3..0....3..2..2....3..2..2....2..2..1....3..2..0....3..1..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Crossrefs

Row 3 of A229774.

Formula

Empirical: a(n) = (1/120)*n^9 + (1/12)*n^8 + (133/360)*n^7 + (371/360)*n^6 + (19/9)*n^5 + (247/72)*n^4 + (403/90)*n^3 + (401/90)*n^2 + (91/30)*n + 1.

Conjectures from Colin Barker, Sep 21 2018: (Start)

G.f.: x*(20 + 122*x + 912*x^2 + 1101*x^3 + 912*x^4 - 125*x^5 + 118*x^6 - 45*x^7 + 10*x^8 - x^9) / (1 - x)^10.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.

(End)