A224025 Number of 3 X n 0..3 arrays with rows nondecreasing and antidiagonals unimodal.

64, 1000, 6796, 32523, 122523, 387729, 1074167, 2679260, 6137666, 13104218, 26368076, 50439449, 92358199, 162782299, 277423483, 458907498, 739147146, 1162327788, 1788617172, 2698724343, 3999445995, 5830352933, 8371784327

Offset

1,1

Comments

Row 3 of A224024.

Links

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

Formula

Empirical: a(n) = (353/181440)*n^9 + (5/126)*n^8 + (12287/30240)*n^7 + (131/60)*n^6 + (64877/8640)*n^5 + (135/8)*n^4 + (998257/45360)*n^3 + (53933/2520)*n^2 + (3421/252)*n - 2 for n>1.

Conjectures from Colin Barker, Aug 26 2018: (Start)

G.f.: x*(64 + 360*x - 324*x^2 + 1883*x^3 - 3447*x^4 + 4386*x^5 - 3748*x^6 + 2193*x^7 - 825*x^8 + 182*x^9 - 18*x^10) / (1 - x)^10.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>11.

(End)

Example

Some solutions for n=3:
..2..2..2....1..2..3....0..0..1....2..3..3....1..1..3....3..3..3....2..2..2
..1..2..2....3..3..3....1..1..3....1..1..1....2..2..2....1..1..2....2..3..3
..3..3..3....0..2..2....2..2..2....1..1..3....0..0..0....1..1..2....0..1..1

Crossrefs

Cf. A224024.

Sequence in context: A224413 A016959 A224392 * A270272 A297612 A000768

Adjacent sequences: A224022 A224023 A224024 * A224026 A224027 A224028

Keyword

nonn

Author

R. H. Hardin, Mar 30 2013

Status

approved