A223633 Number of n X 4 0..1 arrays with rows, antidiagonals and columns unimodal.

11, 121, 801, 3712, 13599, 42109, 114713, 282273, 639165, 1350228, 2689169, 5091414, 9224755, 16081503, 27096217, 44293439, 70470225, 109418622, 166193601, 247432316, 361730919, 520085521, 736404249, 1028097709, 1416755525

Offset

1,1

Comments

Column 4 of A223637.

Links

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

Formula

Empirical: a(n) = (1/112)*n^8 - (1/72)*n^7 + (203/360)*n^6 + (37/360)*n^5 + (41/144)*n^4 + (901/36)*n^3 - (168481/2520)*n^2 + (5693/60)*n - 45 for n>2.

Conjectures from Colin Barker, Aug 21 2018: (Start)

G.f.: x*(11 + 22*x + 108*x^2 - 65*x^3 + 249*x^4 - 74*x^5 + 92*x^6 + 18*x^7 + 9*x^8 - 11*x^9 + x^10) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>11.

(End)

Example

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

Crossrefs

Cf. A223637.

Sequence in context: A262468 A221964 A223640 * A223616 A223665 A068179

Adjacent sequences: A223630 A223631 A223632 * A223634 A223635 A223636

Keyword

nonn

Author

R. H. Hardin, Mar 24 2013

Status

approved