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

Author

R. H. Hardin, Mar 24 2013

Keywords

• nonn

Comments

Column 4 of A223620.

Examples

			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
		

Links

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

Crossrefs

Cf. A223620.

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)