A223681 Number of 3 X n 0..1 arrays with rows and antidiagonals unimodal.

8, 64, 316, 1118, 3177, 7745, 16857, 33615, 62518, 109838, 184042, 296260, 460799, 695703, 1023359, 1471149, 2072148, 2865868, 3899048, 5226490, 6911941, 9029021, 11662197, 14907803, 18875106, 23687418, 29483254, 36417536, 44662843, 54410707

Offset

1,1

Comments

Row 3 of A223680.

Links

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

Formula

Empirical: a(n) = (23/360)*n^6 + (31/120)*n^5 + (17/9)*n^4 + (23/24)*n^3 + (917/360)*n^2 + (77/60)*n + 1.

Conjectures from Colin Barker, Aug 22 2018: (Start)

G.f.: x*(8 + 8*x + 36*x^2 - 30*x^3 + 27*x^4 - 4*x^5 + x^6) / (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>7.

(End)

Example

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

Crossrefs

Cf. A223680.

Sequence in context: A188741 A188993 A355840 * A189065 A189190 A188875

Adjacent sequences: A223678 A223679 A223680 * A223682 A223683 A223684

Keyword

nonn

Author

R. H. Hardin, Mar 25 2013

Status

approved