A222001 - OEIS

%I #10 Aug 14 2018 08:58:06

%S 6,12,22,37,58,86,122,167,222,288,366,457,562,682,818,971,1142,1332,

%T 1542,1773,2026,2302,2602,2927,3278,3656,4062,4497,4962,5458,5986,

%U 6547,7142,7772,8438,9141,9882,10662,11482,12343,13246,14192,15182,16217,17298

%N Number of n X 3 arrays with each row a permutation of 1..3 having at least as many downsteps as the preceding row, with rows in lexicographically nonincreasing order.

%H R. H. Hardin, <a href="/A222001/b222001.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).

%F Conjectures from _Colin Barker_, Aug 14 2018: (Start)

%F G.f.: x*(6 - 12*x + 10*x^2 - 3*x^3) / (1 - x)^4.

%F a(n) = 2 + (1 + n)*(2 + n)*(3 + n) / 6.

%F (End)

%e Some solutions for n=3:

%e ..1..3..2....3..1..2....2..3..1....2..1..3....2..3..1....3..1..2....1..2..3

%e ..1..3..2....3..1..2....2..3..1....2..1..3....1..3..2....2..3..1....1..2..3

%e ..1..3..2....3..1..2....2..1..3....2..1..3....1..3..2....1..3..2....1..2..3

%Y Column 3 of A222005.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 03 2013