A222156 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.

24, 277, 2132, 12521, 60344, 249641, 913748, 3023603, 9190984, 25981835, 68967340, 173242095, 414433320, 949144335, 2090284620, 4443280530, 9145850640, 18279915390, 35563612920, 67490348310, 125168633040, 227242504470

Offset

1,1

Comments

Column 4 of A222159.

Links

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

Formula

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.

Example

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

Crossrefs

Cf. A222159.

Sequence in context: A014809 A007191 A097340 * A297604 A001496 A055754

Adjacent sequences: A222153 A222154 A222155 * A222157 A222158 A222159

Keyword

nonn

Author

R. H. Hardin, Feb 10 2013

Status

approved