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

1,1

Comments

Column 4 of A223644.

Links

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

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)

Example

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

Crossrefs

Cf. A223644.

Sequence in context: A223392 A262468 A221964 * A223633 A223616 A223665

Adjacent sequences: A223637 A223638 A223639 * A223641 A223642 A223643

Keyword

nonn

Author

R. H. Hardin, Mar 24 2013

Status

approved