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

1,1

Comments

Column 4 of A221623.

Links

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

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)

Example

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

Crossrefs

Cf. A221623.

Sequence in context: A018092 A331931 A227750 * A267166 A016326 A287994

Adjacent sequences: A221616 A221617 A221618 * A221620 A221621 A221622

Keyword

nonn

Author

R. H. Hardin, Jan 21 2013

Status

approved