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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.
1
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 03 2013
STATUS
approved