A201445 Number of n X 2 0..3 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

6, 2, 21, 9, 56, 13, 110, 32, 198, 41, 315, 78, 480, 94, 684, 155, 950, 180, 1265, 271, 1656, 307, 2106, 434, 2646, 483, 3255, 652, 3968, 716, 4760, 933, 5670, 1014, 6669, 1285, 7800, 1385, 9030, 1716, 10406, 1837, 11891, 2234, 13536, 2378, 15300, 2847

Offset

1,1

Comments

Column 2 of A201451.

Links

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

Formula

Empirical: a(n) = a(n-2) +3*a(n-4) -3*a(n-6) -3*a(n-8) +3*a(n-10) +a(n-12) -a(n-14).

Subsequences for n modulo 4 = 1,2,3,0:

p=(n+3)/4: a(n) = 8*p^3 - 2*p^2

q=(n+2)/4: a(n) = (4/3)*q^3 + (1/2)*q^2 + (1/6)*q

r=(n+1)/4: a(n) = 8*r^3 + 10*r^2 + 3*r

s=(n+0)/4: a(n) = (4/3)*s^3 + (7/2)*s^2 + (19/6)*s + 1.

Empirical g.f.: x*(6 + 2*x + 15*x^2 + 7*x^3 + 17*x^4 - 2*x^5 + 9*x^6 - 2*x^7 + x^8 + 3*x^9 + x^11 - x^13) / ((1 - x)^4*(1 + x)^4*(1 + x^2)^3). - Colin Barker, May 23 2018

Example

Some solutions for n=10:
..0..0....0..0....0..1....0..1....0..2....0..0....0..0....0..0....0..1....0..0
..0..1....0..1....0..1....0..1....0..2....0..1....0..1....0..0....0..1....0..1
..0..2....0..1....0..2....0..2....0..2....0..1....0..2....0..1....0..1....0..2
..0..2....0..2....0..2....0..2....0..2....0..1....0..2....1..1....0..2....0..2
..1..2....1..2....0..2....0..2....0..2....1..1....1..2....1..1....0..2....1..2
..1..2....1..2....1..2....1..3....1..3....2..2....1..3....2..2....1..2....1..2
..1..2....1..2....1..2....1..3....1..3....2..3....1..3....2..3....1..3....1..3
..1..3....2..3....1..3....1..3....1..3....2..3....1..3....2..3....2..3....1..3
..3..3....3..3....3..3....2..3....1..3....2..3....2..3....2..3....2..3....2..3
..3..3....3..3....3..3....2..3....1..3....3..3....2..3....3..3....3..3....3..3

Crossrefs

Cf. A201451.

Sequence in context: A277275 A213503 A169632 * A090033 A036173 A142707

Adjacent sequences: A201442 A201443 A201444 * A201446 A201447 A201448

Keyword

nonn

Author

R. H. Hardin, Dec 01 2011

Status

approved