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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 2 of A201277.

LINKS

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

FORMULA

Empirical: 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.

Empirical g.f.: 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

Cf. A201277.

Sequence in context: A127397 A284048 A326119 * A324779 A167808 A161353

Adjacent sequences:  A201268 A201269 A201270 * A201272 A201273 A201274

KEYWORD

nonn

AUTHOR

R. H. Hardin, Nov 29 2011

STATUS

approved

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Last modified July 12 04:30 EDT 2020. Contains 335658 sequences. (Running on oeis4.)