A223616 Number of n X 4 0..1 arrays with rows and columns unimodal.

11, 121, 876, 4466, 17594, 57238, 160883, 403159, 921181, 1951247, 3879910, 7312800, 13164932, 22776596, 38059285, 61676477, 97264447, 149698645, 225411536, 332768158, 482506014, 688246274, 967083623, 1340262451, 1833947441

Offset

1,1

Comments

Column 4 of A223620.

Links

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

Formula

Empirical: a(n) = (1/112)*n^8 + (79/1260)*n^7 + (59/180)*n^6 + (299/360)*n^5 + (259/144)*n^4 + (821/360)*n^3 + (7219/2520)*n^2 + (767/420)*n + 1.

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

G.f.: x*(11 + 22*x + 183*x^2 + 14*x^3 + 158*x^4 - 56*x^5 + 35*x^6 - 8*x^7 + x^8) / (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>9.

(End)

Example

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

Crossrefs

Cf. A223620.

Sequence in context: A221964 A223640 A223633 * A223665 A068179 A293891

Adjacent sequences: A223613 A223614 A223615 * A223617 A223618 A223619

Keyword

nonn

Author

R. H. Hardin, Mar 24 2013

Status

approved