A224002 Number of 4 X n 0..2 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

81, 793, 2980, 7927, 17929, 36845, 71061, 130767, 231730, 397675, 663404, 1078800, 1713877, 2665051, 4062821, 6081063, 8948154, 12960157, 18496312, 26037092, 36185097, 49689073, 67471357, 90659063, 120619338, 158999031, 207769132

Offset: 1

Author

R. H. Hardin, Mar 30 2013

Keywords

• nonn

Comments

Row 4 of A223999.

Examples

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

Links

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

Crossrefs

Cf. A223999.

Formula

Empirical: a(n) = (1/2880)*n^8 + (1/180)*n^7 + (25/288)*n^6 + (169/180)*n^5 + (18649/2880)*n^4 + (4247/90)*n^3 + (2719/16)*n^2 - (6649/30)*n - 17 for n>4.

Conjectures from Colin Barker, Aug 25 2018: (Start)

G.f.: x*(81 + 64*x - 1241*x^2 + 2851*x^3 - 2540*x^4 + 248*x^5 + 1398*x^6 - 1380*x^7 + 796*x^8 - 347*x^9 + 88*x^10 - x^11 - 3*x^12) / (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>13.

(End)