A221619 Number of n X 4 arrays with each row a permutation of 1..4 having at least as many downsteps as the preceding row.

24, 410, 6120, 85035, 1130256, 14576404, 183919920, 2282493365, 27960543720, 338950264686, 4073680032984, 48607978698655, 576460247379360, 6800560019808680, 79860630502888416, 934066108666694889

Offset: 1

Author

R. H. Hardin, Jan 21 2013

Keywords

• nonn

Comments

Column 4 of A221623.

Examples

			Some solutions for n=3:
..2..4..1..3....2..1..3..4....3..4..1..2....3..4..2..1....2..1..4..3
..3..2..1..4....2..4..1..3....1..2..4..3....4..1..3..2....3..2..4..1
..4..3..1..2....3..1..2..4....2..4..3..1....4..3..2..1....1..4..3..2
		

Links

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

Crossrefs

Cf. A221623.

Formula

Empirical: a(n) = 24*a(n-1) - 166*a(n-2) + 264*a(n-3) - 121*a(n-4).

Conjectures from Colin Barker, Aug 09 2018: (Start)

G.f.: x*(12 - 11*x)*(2 - 12*x + 11*x^2) / ((1 - x)^2*(1 - 11*x)^2).

a(n) = (4*(4+11^(2+n)) + 5*(1+11^(2+n))*n) / 500.

(End)