A266050 Number of n X 3 integer arrays with each element equal to the number of horizontal and antidiagonal neighbors less than or equal to itself.

2, 12, 20, 54, 120, 284, 660, 1540, 3592, 8376, 19536, 45560, 106256, 247808, 577936, 1347856, 3143456, 7331136, 17097600, 39874848, 92995712, 216883648, 505813824, 1179653824, 2751176576, 6416265856, 14963949568, 34898770048, 81390554368

Offset

1,1

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - 2*a(n-3) - 2*a(n-4).

Empirical g.f.: 2*x*(1 + 4*x - 4*x^2 - 3*x^3) / (1 - 2*x - 2*x^2 + 2*x^3 + 2*x^4). - Colin Barker, Jan 09 2019

Example

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

Crossrefs

Column 3 of A266055.

Sequence in context: A353399 A121859 A145622 * A291698 A174478 A331947

Adjacent sequences: A266047 A266048 A266049 * A266051 A266052 A266053

Keyword

nonn

Author

R. H. Hardin, Dec 20 2015

Status

approved