A224159 Number of 3 X n 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

8, 36, 89, 187, 373, 702, 1252, 2130, 3479, 5486, 8391, 12497, 18181, 25906, 36234, 49840, 67527, 90242, 119093, 155367, 200549, 256342, 324688, 407790, 508135, 628518, 772067, 942269, 1142997, 1378538, 1653622, 1973452, 2343735, 2770714

Offset

1,1

Comments

Row 3 of A224158.

Links

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

Formula

Empirical: a(n) = (1/720)*n^6 + (1/240)*n^5 + (47/144)*n^4 - (3/16)*n^3 + (1111/180)*n^2 - (199/60)*n + 20 for n>2.

Conjectures from Colin Barker, Aug 28 2018: (Start)

G.f.: x*(8 - 20*x + 5*x^2 + 40*x^3 - 47*x^4 - 5*x^5 + 41*x^6 - 27*x^7 + 6*x^8) / (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>9.

(End)

Example

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

Crossrefs

Cf. A224158.

Sequence in context: A321778 A009923 A187287 * A321251 A035006 A245360

Adjacent sequences: A224156 A224157 A224158 * A224160 A224161 A224162

Keyword

nonn

Author

R. H. Hardin, Mar 31 2013

Status

approved