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

1,1

Links

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

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)

Example

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

Crossrefs

Row 3 of A229774.

Sequence in context: A024387 A307173 A101310 * A159648 A353106 A078230

Adjacent sequences: A229772 A229773 A229774 * A229776 A229777 A229778

Keyword

nonn

Author

R. H. Hardin, Sep 29 2013

Status

approved