A223670 Number of 3 X n 0..1 arrays with rows, diagonals and antidiagonals unimodal.

8, 64, 292, 948, 2527, 5913, 12577, 24821, 46068, 81198, 136930, 222250, 348885, 531823, 789879, 1146307, 1629458, 2273484, 3119088, 4214320, 5615419, 7387701, 9606493, 12358113, 15740896, 19866266, 24859854, 30862662, 38032273, 46544107

Offset

1,1

Comments

Row 3 of A223669.

Links

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

Formula

Empirical: a(n) = (23/360)*n^6 - (3/40)*n^5 + (37/18)*n^4 + (119/24)*n^3 - (3103/360)*n^2 + (997/60)*n - 9 for n>1.

Conjectures from Colin Barker, Mar 16 2018: (Start)

G.f.: x*(8 + 8*x + 12*x^2 - 32*x^3 + 63*x^4 - 16*x^5 + 5*x^6 - 2*x^7) / (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>8.

(End)

Example

Some solutions for n=4:
..0..1..1..1....0..1..1..0....0..0..1..1....0..0..0..1....1..0..0..0
..1..1..0..0....0..1..0..0....0..1..0..0....0..0..1..1....0..1..1..1
..0..0..0..0....0..1..1..0....1..0..0..0....0..1..1..0....0..0..0..0

Crossrefs

Cf. A223669.

Sequence in context: A167239 A236554 A173502 * A189618 A189690 A188741

Adjacent sequences: A223667 A223668 A223669 * A223671 A223672 A223673

Keyword

nonn

Author

R. H. Hardin, Mar 25 2013

Status

approved