A201696 Number of n X 4 0..2 arrays with rows and columns lexicographically nondecreasing read forwards and nonincreasing read backwards.

3, 27, 395, 4998, 35390, 167625, 607919, 1826778, 4775228, 11211034, 24167306, 48600665, 92261185, 166831642, 289389192, 484248471, 785251265, 1238574341, 1906133765, 2869671064, 4235613920, 6140811719, 8759254221, 12309889872

Offset

1,1

Comments

Column 4 of A201700.

Links

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

Formula

Empirical: a(n) = (1/907200)*n^10 + (13/20160)*n^9 + (8321/120960)*n^8 + (97/105)*n^7 - (40969/5400)*n^6 + (22681/960)*n^5 - (11661313/362880)*n^4 - (388097/10080)*n^3 + (4320179/16800)*n^2 - (323861/840)*n + 185.

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

G.f.: x*(3 - 6*x + 263*x^2 + 1643*x^3 - 1328*x^4 - 4426*x^5 + 5086*x^6 - 1972*x^7 + 1789*x^8 - 1233*x^9 + 185*x^10) / (1 - x)^11.

a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>11.

(End)

Example

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

Crossrefs

Cf. A201700.

Sequence in context: A141057 A365569 A365586 * A011781 A094577 A221624

Adjacent sequences: A201693 A201694 A201695 * A201697 A201698 A201699

Keyword

nonn

Author

R. H. Hardin, Dec 03 2011

Status

approved