A229449 Number of 6 X n 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

23, 84, 293, 915, 2546, 6374, 14536, 30571, 59969, 110816, 194535, 326723, 528084, 825458, 1252946, 1853131, 2678395, 3792332, 5271257, 7205811, 9702662, 12886302, 16900940, 21912491, 28110661, 35711128, 44957819, 56125283, 69521160, 85488746

Offset

1,1

Links

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

Formula

Empirical: a(n) = (2/15)*n^6 - (5/8)*n^5 + (9/2)*n^4 - (55/8)*n^3 + (283/15)*n^2 - 4*n + 11.

Conjectures from Colin Barker, Sep 17 2018: (Start)

G.f.: x*(23 - 77*x + 188*x^2 - 177*x^3 + 159*x^4 - 31*x^5 + 11*x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Example

Some solutions for n=4.
..0..0..0..0....0..2..2..2....0..2..2..2....0..2..2..2....0..2..2..2
..0..0..0..0....1..0..2..2....0..2..2..2....1..0..2..2....1..0..2..2
..0..0..0..0....2..1..0..0....0..2..2..2....1..1..0..2....1..1..0..2
..1..1..1..1....2..1..0..0....1..0..2..2....2..1..0..0....1..1..1..0
..2..2..2..2....2..2..1..1....1..0..2..2....2..1..0..0....2..1..1..0
..2..2..2..2....2..2..2..2....1..1..0..0....2..1..0..0....2..1..1..1

Crossrefs

Row 6 of A229445.

Sequence in context: A262119 A104068 A304839 * A060456 A056580 A010011

Adjacent sequences: A229446 A229447 A229448 * A229450 A229451 A229452

Keyword

nonn

Author

R. H. Hardin, Sep 23 2013

Status

approved