A188820 Number of n X 5 binary arrays without the pattern 0 1 diagonally or antidiagonally.

32, 169, 432, 841, 1360, 2025, 2800, 3721, 4752, 5929, 7216, 8649, 10192, 11881, 13680, 15625, 17680, 19881, 22192, 24649, 27216, 29929, 32752, 35721, 38800, 42025, 45360, 48841, 52432, 56169, 60016, 64009, 68112, 72361, 76720, 81225, 85840, 90601

Offset

1,1

Comments

Column 5 of A188824.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>5.

Conjectures from Colin Barker, Apr 29 2018: (Start)

G.f.: x*(32 + 105*x + 94*x^2 + 41*x^3 - 16*x^4) / ((1 - x)^3*(1 + x)).

a(n) = 9 - 48*n + 64*n^2 for n even.

a(n) = -48*n + 64*n^2 for n>1 and odd.

(End)

Example

Some solutions for 3 X 5:
..1..1..1..1..0....1..1..1..1..1....0..1..0..1..1....0..1..1..1..1
..0..1..1..0..1....0..1..1..1..0....0..0..0..0..1....1..0..1..1..1
..1..0..0..1..0....1..0..0..0..0....0..0..0..0..0....0..1..0..0..0

Crossrefs

Cf. A188824.

Sequence in context: A302621 A302413 A303180 * A181209 A231299 A029534

Adjacent sequences: A188817 A188818 A188819 * A188821 A188822 A188823

Keyword

nonn

Author

R. H. Hardin, Apr 11 2011

Status

approved