A224258 Number of n X 4 0..2 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

46, 548, 3096, 12467, 41012, 116692, 296646, 688533, 1482310, 2995516, 5735542, 10482777, 18398930, 31165238, 51155680, 81650727, 127097568, 193423162, 288406876, 422119879, 607438872, 860642144, 1202096354, 1657042849, 2256492738, 3038240352, 4048005130, 5340712381

Offset: 1

Author

R. H. Hardin, Apr 02 2013

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Column 4 of A224262.

Formula

Empirical: a(n) = (41/4032)*n^8 + (9/112)*n^7 + (349/480)*n^6 + (69/20)*n^5 + (1325/192)*n^4 + (1571/48)*n^3 + (87503/5040)*n^2 - (21949/420)*n + 43 for n>2.

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

G.f.: x*(46 + 134*x - 180*x^2 + 467*x^3 + 29*x^4 - 416*x^5 + 534*x^6 - 255*x^7 + 61*x^8 - 12*x^9 + 2*x^10) / (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>11.

(End)

Extensions

Name corrected by Andrew Howroyd, Mar 18 2025