A223640 Number of n X 4 0..1 arrays with rows, columns, diagonals and antidiagonals unimodal.

11, 121, 726, 2962, 9808, 28450, 74599, 179991, 404599, 855417, 1714062, 3275798, 6002946, 10596004, 18086161, 29953249, 48273537, 75902131, 116695104, 175776840, 259858436, 377613366, 540116971, 761356699, 1058820379, 1454170173

Offset: 1

Author

R. H. Hardin, Mar 24 2013

Keywords

• nonn

Comments

Column 4 of A223644.

Examples

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

Links

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

Crossrefs

Cf. A223644.

Formula

Empirical: a(n) = (1/112)*n^8 - (19/210)*n^7 + (107/90)*n^6 - (197/40)*n^5 + (2219/144)*n^4 + (5093/120)*n^3 - (868411/2520)*n^2 + (417721/420)*n - 1091 for n>4.

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

G.f.: x*(11 + 22*x + 33*x^2 - 140*x^3 + 508*x^4 - 314*x^5 - 17*x^6 + 432*x^7 - 233*x^8 + 28*x^9 + 56*x^10 - 28*x^11 + 2*x^12) / (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>13.

(End)