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, 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

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000 (terms n = 1..210 from R. H. Hardin)

Formula

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).

G.f.: 1 + 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

Column 3 of A201277.

Sequence in context: A171378 A147478 A147372 * A147440 A146678 A146417

Adjacent sequences: A201269 A201270 A201271 * A201273 A201274 A201275

Keyword

nonn,easy

Author

R. H. Hardin, Nov 29 2011

Extensions

a(0)=1 prepended by Alois P. Heinz, Mar 18 2024

Status

approved