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

1,1

Comments

Row 4 of A223999.

Links

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

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)

Example

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

Crossrefs

Cf. A223999.

Sequence in context: A066431 A206086 A356534 * A253461 A247842 A273233

Adjacent sequences: A223999 A224000 A224001 * A224003 A224004 A224005

Keyword

nonn

Author

R. H. Hardin, Mar 30 2013

Status

approved