A207399 Number of n X 4 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically.

9, 81, 289, 729, 1521, 2809, 4761, 7569, 11449, 16641, 23409, 32041, 42849, 56169, 72361, 91809, 114921, 142129, 173889, 210681, 253009, 301401, 356409, 418609, 488601, 567009, 654481, 751689, 859329, 978121, 1108809, 1252161, 1408969

Offset

1,1

Comments

Column 4 of A207403.

Links

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

Formula

Empirical: a(n) = n^4 + 6*n^3 + 7*n^2 - 6*n + 1.

Conjectures from Colin Barker, Mar 05 2018: (Start)

G.f.: x*(9 + 36*x - 26*x^2 + 4*x^3 + x^4) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)

Example

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

Crossrefs

Cf. A207403.

Sequence in context: A207244 A207064 A207119 * A207904 A207748 A208035

Adjacent sequences: A207396 A207397 A207398 * A207400 A207401 A207402

Keyword

nonn

Author

R. H. Hardin, Feb 17 2012

Status

approved