A201271 Number of n X 2 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, 3, 5, 4, 12, 16, 9, 27, 33, 16, 48, 56, 25, 75, 85, 36, 108, 120, 49, 147, 161, 64, 192, 208, 81, 243, 261, 100, 300, 320, 121, 363, 385, 144, 432, 456, 169, 507, 533, 196, 588, 616, 225, 675, 705, 256, 768, 800, 289, 867, 901, 324, 972, 1008, 361, 1083, 1121, 400, 1200

Offset

0,2

Links

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

Formula

a(n) = 3*a(n-3) -3*a(n-6) +a(n-9).

Subsequences for n modulo 3 = 1,2,0:

p=(n+2)/3: a(n) = 3*p^2

q=(n+1)/3: a(n) = 3*q^2 + 2*q

r=(n+0)/3: a(n) = r^2 + 2*r + 1.

G.f.: 1+x*(3 + 5*x + 4*x^2 + 3*x^3 + x^4 - 3*x^5 + x^8) / ((1 - x)^3*(1 + x + x^2)^3). - Colin Barker, May 22 2018

Example

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

Crossrefs

Column 2 of A201277.

Sequence in context: A127397 A284048 A326119 * A324779 A167808 A161353

Adjacent sequences: A201268 A201269 A201270 * A201272 A201273 A201274

Keyword

nonn,easy

Author

R. H. Hardin, Nov 29 2011

Extensions

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

Status

approved