A223839 Number of 3 X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

4, 16, 48, 118, 255, 503, 926, 1614, 2690, 4318, 6712, 10146, 14965, 21597, 30566, 42506, 58176, 78476, 104464, 137374, 178635, 229891, 293022, 370166, 463742, 576474, 711416, 871978, 1061953, 1285545, 1547398, 1852626, 2206844, 2616200

Offset

1,1

Comments

Row 3 of A223838.

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 + (29/144)*n^4 + (11/48)*n^3 + (1007/360)*n^2 - (37/30)*n + 2.

Conjectures from Colin Barker, Aug 23 2018: (Start)

G.f.: x*(2 - 2*x + x^2)*(2 - 4*x + 5*x^2 - 4*x^3 + 2*x^4) / (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..0....0..0..0....0..1..0....1..0..0....1..0..0....0..1..0....0..1..1
..1..1..0....0..1..0....0..1..0....1..1..1....1..1..0....0..1..1....0..1..1
..1..1..1....0..1..0....1..1..0....1..1..1....1..1..0....1..1..1....0..1..1

Crossrefs

Cf. A223838.

Sequence in context: A261977 A100625 A203248 * A071009 A210066 A131126

Adjacent sequences: A223836 A223837 A223838 * A223840 A223841 A223842

Keyword

nonn

Author

R. H. Hardin, Mar 27 2013

Status

approved