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A224025 Number of 3 X n 0..3 arrays with rows nondecreasing and antidiagonals unimodal. 1
64, 1000, 6796, 32523, 122523, 387729, 1074167, 2679260, 6137666, 13104218, 26368076, 50439449, 92358199, 162782299, 277423483, 458907498, 739147146, 1162327788, 1788617172, 2698724343, 3999445995, 5830352933, 8371784327 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 13 16:10 EDT 2019. Contains 327966 sequences. (Running on oeis4.)