A223963 Number of 3 X n 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

64, 707, 3471, 12311, 36028, 92734, 217144, 471994, 965172, 1874532, 3482781, 6225291, 10754192, 18022648, 29393806, 46779538, 72814768, 111073890, 166336539, 244910775, 355022580, 507281450, 715232788, 996008770, 1371090364

Offset

1,1

Comments

Row 3 of A223961.

Links

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

Formula

Empirical: a(n) = (1/8640)*n^9 + (1/320)*n^8 + (503/10080)*n^7 + (659/1440)*n^6 + (3013/960)*n^5 + (37141/2880)*n^4 + (106019/2160)*n^3 - (18977/720)*n^2 + (2711/70)*n - 6 for n>2.

Conjectures from Colin Barker, Aug 24 2018: (Start)

G.f.: x*(64 + 67*x - 719*x^2 + 1736*x^3 - 2287*x^4 + 2271*x^5 - 2070*x^6 + 1632*x^7 - 910*x^8 + 311*x^9 - 58*x^10 + 5*x^11) / (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>12.

(End)

Example

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

Crossrefs

Cf. A223961.

Sequence in context: A119287 A318023 A320408 * A372844 A303726 A305229

Adjacent sequences: A223960 A223961 A223962 * A223964 A223965 A223966

Keyword

nonn

Author

R. H. Hardin, Mar 29 2013

Status

approved