A296315 Number of n X 3 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 1 neighboring 1.

3, 11, 32, 96, 295, 902, 2747, 8380, 25577, 78021, 238029, 726211, 2215568, 6759403, 20622067, 62915288, 191946374, 585603549, 1786600798, 5450687951, 16629344149, 50733978916, 154782809780, 472222339285, 1440689299042, 4395356771500

Offset

1,1

Links

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

Formula

Empirical: a(n) = a(n-1) + 4*a(n-2) + 6*a(n-3) + 3*a(n-4) - 3*a(n-6) + a(n-7) - 3*a(n-9) + a(n-11).

Empirical g.f.: x*(3 + 8*x + 9*x^2 + 2*x^3 - 4*x^4 - 2*x^5 + 2*x^6 - 3*x^7 - 3*x^8 + x^9 + x^10) / ((1 + x^2 - x^3)*(1 - x - 5*x^2 - 4*x^3 + x^4 - x^5 - 2*x^6 + x^7 + x^8)). - Colin Barker, Feb 23 2019

Example

Some solutions for n=5:
..0..0..0. .0..1..1. .0..1..0. .1..1..0. .0..0..0. .0..0..0. .0..0..0
..0..0..0. .0..0..0. .0..1..0. .0..0..1. .0..1..0. .0..0..0. .1..1..0
..0..0..0. .1..0..0. .0..0..0. .0..1..0. .1..0..0. .1..0..0. .0..0..0
..0..0..0. .1..0..1. .0..0..0. .0..0..1. .0..1..0. .1..0..0. .0..0..1
..1..1..0. .0..1..0. .0..1..1. .0..1..0. .1..0..0. .0..1..1. .0..0..1

Crossrefs

Column 3 of A296320.

Sequence in context: A141211 A353065 A321645 * A125671 A034561 A131747

Adjacent sequences: A296312 A296313 A296314 * A296316 A296317 A296318

Keyword

nonn

Author

R. H. Hardin, Dec 10 2017

Status

approved