A224043 Number of 7 X n 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

128, 987, 2419, 4160, 6321, 9125, 12856, 17875, 24623, 33686, 45837, 62087, 83746, 112495, 150470, 200359, 265513, 350072, 459107, 598779, 776516, 1001209, 1283428, 1635659, 2072563, 2611258, 3271625, 4076639, 5052726, 6230147, 7643410, 9331711

Offset

1,1

Comments

Row 7 of A224038.

Links

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

Formula

Empirical: a(n) = (1/5040)*n^7 + (17/360)*n^5 + (13/24)*n^4 + (5767/720)*n^3 + (1919/24)*n^2 + (37901/70)*n + 143 for n>5.

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

G.f.: x*(128 - 37*x - 1893*x^2 + 5276*x^3 - 5539*x^4 + 1495*x^5 + 1526*x^6 - 1101*x^7 + 65*x^8 + 155*x^9 - 160*x^10 + 117*x^11 - 31*x^12) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>13.

(End)

Example

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

Crossrefs

Cf. A224038.

Sequence in context: A188151 A372094 A297643 * A188841 A188704 A297344

Adjacent sequences: A224040 A224041 A224042 * A224044 A224045 A224046

Keyword

nonn

Author

R. H. Hardin, Mar 30 2013

Status

approved