A222002 Number of n X 4 arrays with each row a permutation of 1..4 having at least as many downsteps as the preceding row, with rows in lexicographically nonincreasing order.

24, 157, 704, 2470, 7328, 19228, 45894, 101543, 211070, 416275, 784864, 1423138, 2493494, 4238102, 7010394, 11316307, 17867564, 27649657, 42007616, 62753110, 92296932, 133811472, 191428382, 270477287, 377772098, 521952239, 713886912

Offset

1,1

Comments

Column 4 of A222005.

Links

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

Formula

Empirical: a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11).

Empirical g.f.: x*(24 - 107*x + 297*x^2 - 599*x^3 + 893*x^4 - 968*x^5 + 750*x^6 - 405*x^7 + 145*x^8 - 31*x^9 + 3*x^10) / (1 - x)^11. - Colin Barker, Aug 14 2018

Example

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

Crossrefs

Cf. A222005.

Sequence in context: A277984 A125334 A126492 * A240268 A231341 A186862

Adjacent sequences: A221999 A222000 A222001 * A222003 A222004 A222005

Keyword

nonn

Author

R. H. Hardin, Feb 03 2013

Status

approved