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

Author

R. H. Hardin, Mar 25 2013

Keywords

• nonn

Comments

Row 3 of A223669.

Examples

			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
		

Links

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

Crossrefs

Cf. A223669.

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)