%I #7 Mar 15 2023 14:34:45
%S 24,277,2132,12521,60344,249641,913748,3023603,9190984,25981835,
%T 68967340,173242095,414433320,949144335,2090284620,4443280530,
%U 9145850640,18279915390,35563612920,67490348310,125168633040,227242504470
%N 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 nondecreasing order.
%C Column 4 of A222159.
%H R. H. Hardin, <a href="/A222156/b222156.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/3201186852864000)*n^18 + (1/19760412672000)*n^17 + (251/62768369664000)*n^16 + (29/145297152000)*n^15 + (217031/31384184832000)*n^14 + (43447/249080832000)*n^13 + (2169611/658409472000)*n^12 + (3183331/67060224000)*n^11 + (231419681/438939648000)*n^10 + (36901183/8128512000)*n^9 + (146423897891/4828336128000)*n^8 + (1499409367/9580032000)*n^7 + (14551383635479/23538138624000)*n^6 + (400802254661/217945728000)*n^5 + (5254041870533/1307674368000)*n^4 + (112591393237/18162144000)*n^3 + (17776195417/2806876800)*n^2 + (46566643/12252240)*n + 1.
%e Some solutions for n=3
%e ..1..2..4..3....3..2..4..1....2..3..1..4....2..1..3..4....1..4..3..2
%e ..4..1..3..2....4..2..3..1....4..1..3..2....2..3..4..1....1..4..3..2
%e ..4..3..1..2....4..2..3..1....4..3..1..2....3..1..2..4....2..4..3..1
%Y Cf. A222159.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 10 2013
