A208114 Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 0 1 1 vertically.

9, 81, 225, 625, 1225, 2401, 3969, 6561, 9801, 14641, 20449, 28561, 38025, 50625, 65025, 83521, 104329, 130321, 159201, 194481, 233289, 279841, 330625, 390625, 455625, 531441, 613089, 707281, 808201, 923521, 1046529, 1185921, 1334025

Offset

1,1

Comments

Column 4 of A208118.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - 6*a(n-3) + 6*a(n-5) - 2*a(n-6) - 2*a(n-7) + a(n-8).

Conjectures from Colin Barker, Jun 28 2018: (Start)

G.f.: x*(9 + 63*x + 45*x^2 + 67*x^3 + 11*x^4 - 3*x^5 - x^6 + x^7) / ((1 - x)^5*(1 + x)^3).

a(n) = n^4 + 4*n^3 + 6*n^2 + 4*n + 1 for n even.

a(n) = n^4 + 4*n^3 + 4*n^2 for n odd.

(End)

Example

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

Crossrefs

Cf. A208118.

Sequence in context: A207758 A016946 A144938 * A208119 A207369 A208014

Adjacent sequences: A208111 A208112 A208113 * A208115 A208116 A208117

Keyword

nonn

Author

R. H. Hardin, Feb 23 2012

Status

approved