A224137 - OEIS

A224137

Number of 6 X n 0..1 arrays with rows nondecreasing and antidiagonals unimodal.

64, 729, 2692, 6392, 12874, 24095, 42832, 72888, 119424, 189263, 291226, 436500, 639038, 915991, 1288172, 1780552, 2422788, 3249783, 4302278, 5627476, 7279698, 9321071, 11822248, 14863160, 18533800, 22935039, 28179474, 34392308, 41712262

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OFFSET

1,1

COMMENTS

Row 6 of A224133.

LINKS

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

FORMULA

Empirical: a(n) = (2/45)*n^6 + (8/15)*n^5 + (181/36)*n^4 + 28*n^3 + (19247/180)*n^2 + (3952/15)*n - 120 for n>4.

Conjectures from Colin Barker, Aug 27 2018: (Start)

G.f.: x*(64 + 281*x - 1067*x^2 + 617*x^3 + 1387*x^4 - 1840*x^5 + 160*x^6 + 696*x^7 - 172*x^8 - 154*x^9 + 60*x^10) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>11.

(End)

EXAMPLE

Some solutions for n=3:

..0..0..1....0..0..1....0..1..1....0..0..1....0..0..0....0..0..0....0..0..1

..1..1..1....0..1..1....0..0..1....0..0..0....0..0..0....0..1..1....0..1..1

..0..1..1....1..1..1....0..0..1....0..0..1....0..1..1....0..0..1....0..1..1

..0..1..1....0..0..1....0..1..1....0..0..0....1..1..1....0..0..0....1..1..1

..1..1..1....0..1..1....0..0..1....0..0..1....1..1..1....0..0..1....1..1..1

..0..0..0....0..1..1....0..0..1....0..0..0....0..0..1....0..0..1....0..1..1

CROSSREFS

Cf. A224133.

Sequence in context: A161860 A195249 A223953 * A016899 A250364 A346638

Adjacent sequences: A224134 A224135 A224136 * A224138 A224139 A224140

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 31 2013

STATUS

approved