A201272 Number of n X 3 0..2 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

1, 4, 7, 14, 21, 41, 54, 86, 120, 168, 218, 307, 377, 496, 621, 776, 937, 1177, 1380, 1676, 1984, 2344, 2716, 3221, 3665, 4260, 4875, 5570, 6285, 7201, 8026, 9074, 10152, 11344, 12566, 14071, 15449, 17136, 18865, 20748, 22673, 24977, 27112, 29656, 32256, 35056

Offset

1,2

Comments

Column 3 of A201277.

Links

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

Formula

Empirical: a(n) = 2*a(n-2) + 2*a(n-3) - a(n-4) - 4*a(n-5) + 2*a(n-7) - 2*a(n-9) + 4*a(n-11) + a(n-12) - 2*a(n-13) - 2*a(n-14) + a(n-16).

Empirical g.f.: x*(1 + 4*x + 5*x^2 + 4*x^3 + 7*x^5 + 7*x^6 + 2*x^7 - x^8 + x^9 + 4*x^10 + x^11 - 2*x^12 - 2*x^13 + x^15) / ((1 - x)^5*(1 + x)^3*(1 - x + x^2)*(1 + x + x^2)^3). - Colin Barker, Mar 02 2018

Example

Some solutions for n=5:
..0..0..0....0..0..0....0..0..1....0..0..0....0..0..1....0..0..2....0..0..1
..0..0..2....0..0..1....0..0..2....0..0..1....0..0..1....0..0..2....0..1..1
..1..1..2....1..1..2....0..1..2....1..1..1....0..1..2....0..1..2....0..1..2
..1..1..2....1..1..2....1..1..2....1..2..2....1..1..2....1..1..2....0..1..2
..1..2..2....2..2..2....1..2..2....2..2..2....2..2..2....1..1..2....2..2..2

Crossrefs

Cf. A201277.

Sequence in context: A171378 A147478 A147372 * A147440 A146678 A146417

Adjacent sequences: A201269 A201270 A201271 * A201273 A201274 A201275

Keyword

nonn

Author

R. H. Hardin, Nov 29 2011

Status

approved