A224041 Number of 5 X n 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

32, 144, 298, 488, 734, 1064, 1505, 2091, 2864, 3875, 5185, 6866, 9002, 11690, 15041, 19181, 24252, 30413, 37841, 46732, 57302, 69788, 84449, 101567, 121448, 144423, 170849, 201110, 235618, 274814, 319169, 369185, 425396, 488369, 558705, 637040

Offset

1,1

Comments

Row 5 of A224038.

Links

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

Formula

Empirical: a(n) = (1/120)*n^5 + (1/24)*n^4 + (25/24)*n^3 + (227/24)*n^2 + (1289/20)*n - 7 for n>3.

Conjectures from Colin Barker, Aug 26 2018: (Start)

G.f.: x*(32 - 48*x - 86*x^2 + 220*x^3 - 124*x^4 - 12*x^5 + 9*x^6 + 17*x^7 - 7*x^8) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>9.

(End)

Example

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

Crossrefs

Cf. A224038.

Sequence in context: A100164 A048191 A363531 * A188839 A188702 A297342

Adjacent sequences: A224038 A224039 A224040 * A224042 A224043 A224044

Keyword

nonn

Author

R. H. Hardin, Mar 30 2013

Status

approved