A209042 Number of n X 3 0..3 arrays with no element equal the average of immediate neighbors vertically above and horizontally left of it.

36, 1300, 47700, 1752148, 64369764, 2364812680, 86878417604, 3191736905988, 117257942776700, 4307819083344444, 158260539240359944, 5814171346741659592, 213600867349885236600, 7847262801829583566600, 288292525423375500733688

Offset: 1

Author

R. H. Hardin, Mar 04 2012

Keywords

• nonn

Comments

Column 3 of A209047.

Examples

			Some solutions for n=4
..0..1..0....0..1..2....2..1..2....2..0..1....1..0..2....1..3..0....1..0..1
..3..3..2....3..3..0....3..0..2....0..2..0....3..2..1....2..1..3....0..1..3
..1..3..1....0..1..1....2..0..0....1..2..2....1..0..3....0..1..0....1..2..1
..2..3..3....3..3..1....1..3..0....3..0..0....3..0..1....1..2..0....0..2..3
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210
• Robert Israel, Maple-assisted proof of empirical formula

Crossrefs

Cf. A209047.

Formula

Empirical: a(n) = 23*a(n-1) +491*a(n-2) +570*a(n-3) -2219*a(n-4) -7882*a(n-5) -12517*a(n-6) -6376*a(n-7) -1205*a(n-8) -6747*a(n-9) +4080*a(n-10) +7811*a(n-11) -4675*a(n-12) +1790*a(n-13) +2576*a(n-14) -2905*a(n-15) +513*a(n-16) +621*a(n-17) -27*a(n-18) -81*a(n-19).

Formula confirmed by Robert Israel, Apr 03 2018 (see link).