A229441 Number of n X 4 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

6, 14, 37, 109, 324, 915, 2402, 5843, 13229, 28071, 56234, 107080, 194989, 341334, 576993, 945488, 1506848, 2342300, 3559899, 5301215, 7749202, 11137381, 15760476, 21986649, 30271487, 41173901, 55374104, 73693842, 97119059, 126825184

Offset: 1

Author

R. H. Hardin, Sep 23 2013

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Column 4 of A229445.

Formula

Empirical: a(n) = (1/5760)*n^8 + (1/2016)*n^7 + (1/576)*n^6 + (11/360)*n^5 + (409/5760)*n^4 + (49/288)*n^3 + (41/96)*n^2 + (2771/840)*n + 2.

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

G.f.: x*(6 - 40*x + 127*x^2 - 224*x^3 + 255*x^4 - 177*x^5 + 77*x^6 - 19*x^7 + 2*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)