A223682 Number of 4 X n 0..1 arrays with rows and antidiagonals unimodal.

16, 256, 2032, 9822, 35509, 105995, 275775, 646407, 1395174, 2815594, 5372794, 9777124, 17079747, 28794301, 47049089, 74774613, 115931628, 175785252, 261231028, 381179194, 547003777, 773063487, 1077301747, 1481933555

Offset

1,1

Comments

Row 4 of A223680.

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 + (121/120)*n^6 + (71/36)*n^5 + (475/48)*n^4 - (1757/180)*n^3 + (8893/840)*n^2 - (569/84)*n + 9.

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

G.f.: x*(16 + 112*x + 304*x^2 - 594*x^3 + 775*x^4 - 442*x^5 + 216*x^6 - 36*x^7 + 9*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=3:
..1..1..0....0..0..1....1..0..0....0..0..0....0..1..1....1..1..0....0..1..0
..1..1..0....0..0..0....0..1..0....1..1..0....0..1..0....0..1..0....0..0..1
..0..1..1....0..0..0....1..0..0....0..1..1....0..0..0....1..1..0....1..1..1
..0..0..1....0..1..1....0..1..0....1..1..0....0..1..1....1..0..0....0..1..0

Crossrefs

Cf. A223680.

Sequence in context: A188994 A208075 A223641 * A189066 A189191 A188876

Adjacent sequences: A223679 A223680 A223681 * A223683 A223684 A223685

Keyword

nonn

Author

R. H. Hardin, Mar 25 2013

Status

approved