A221620 Number of n X 5 arrays with each row a permutation of 1..5 having at least as many downsteps as the preceding row.

120, 10055, 738150, 51149685, 3451956516, 230141263315, 15258126049410, 1009051056050225, 66655625407012320, 4400938611593606031, 290509268912775739710, 19174945298440265379565, 1265583745617128902739100

Offset

1,1

Comments

Column 5 of A221623.

Links

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

Formula

Empirical: a(n) = 120*a(n-1) - 4345*a(n-2) + 52950*a(n-3) - 93340*a(n-4) + 44616*a(n-5).

Empirical g.f.: x*(120 - 4345*x + 52950*x^2 - 93340*x^3 + 44616*x^4) / ((1 - x)^2*(1 - 26*x)^2*(1 - 66*x)). - Colin Barker, Aug 09 2018

Example

Some solutions for n=3:
..1..2..3..4..5....1..2..4..3..5....1..2..4..3..5....1..2..3..5..4
..4..5..1..3..2....1..2..5..4..3....4..3..1..2..5....1..2..5..3..4
..5..1..2..4..3....3..5..4..1..2....5..3..4..1..2....1..3..4..5..2

Crossrefs

Cf. A221623.

Sequence in context: A156411 A076005 A218503 * A299954 A226804 A104592

Adjacent sequences: A221617 A221618 A221619 * A221621 A221622 A221623

Keyword

nonn

Author

R. H. Hardin, Jan 21 2013

Status

approved