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

Author

R. H. Hardin, Dec 01 2011

Keywords

• nonn

Comments

Column 2 of A201451.

Examples

			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
		

Links

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

Crossrefs

Cf. A201451.

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