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A224043 Number of 7 X n 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A218070 A188151 A297643 * A188841 A188704 A297344

Adjacent sequences:  A224040 A224041 A224042 * A224044 A224045 A224046

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 30 2013

STATUS

approved

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Last modified February 24 22:04 EST 2020. Contains 332216 sequences. (Running on oeis4.)