A224355 Number of 4 X n 0..2 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

81, 1296, 5880, 19608, 57387, 151010, 363392, 810436, 1693423, 3344982, 6292120, 11340202, 19682181, 33037788, 53827802, 85388930, 132235237, 200372476, 297672078, 434311972, 623291815, 881030622, 1228055196, 1689788168

Offset

1,1

Comments

Row 4 of A224353.

Links

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

Formula

Empirical: a(n) = (41/4032)*n^8 + (9/112)*n^7 + (239/288)*n^6 + (109/24)*n^5 + (12079/576)*n^4 + (39/16)*n^3 + (310151/1008)*n^2 - (21299/84)*n + 142 for n>3.

Conjectures from Colin Barker, Aug 29 2018: (Start)

G.f.: x*(81 + 567*x - 2868*x^2 + 6540*x^3 - 6063*x^4 - 415*x^5 + 7550*x^6 - 8564*x^7 + 4918*x^8 - 1584*x^9 + 262*x^10 - 14*x^11) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>12.

(End)

Example

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

Crossrefs

Cf. A224353.

Sequence in context: A231994 A236790 A232876 * A016768 A224014 A059977

Adjacent sequences: A224352 A224353 A224354 * A224356 A224357 A224358

Keyword

nonn

Author

R. H. Hardin, Apr 04 2013

Status

approved