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

1,1

Comments

Column 3 of A209047.

Links

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

Robert Israel, Maple-assisted proof of empirical formula

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).

Example

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

Crossrefs

Cf. A209047.

Sequence in context: A009980 A041613 A255821 * A283729 A203333 A226772

Adjacent sequences: A209039 A209040 A209041 * A209043 A209044 A209045

Keyword

nonn

Author

R. H. Hardin, Mar 04 2012

Status

approved