A297584 Number of 3 X n 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 4 neighboring 1's.

1, 9, 36, 72, 188, 688, 2085, 5497, 16037, 49553, 144816, 413800, 1217824, 3611968, 10551977, 30756729, 90335433, 265402081, 776832420, 2274331728, 6670542132, 19558546400, 57298805509, 167902287673, 492193237461, 1442605306409

Offset

1,2

Links

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

Formula

Empirical: a(n) = a(n-1) + a(n-2) + 8*a(n-3) + 18*a(n-4) + a(n-5) - 11*a(n-6) - 12*a(n-7) - a(n-8).

Empirical g.f.: x*(1 + 8*x + 26*x^2 + 19*x^3 - 10*x^4 - 23*x^5 - 13*x^6 - x^7) / (1 - x - x^2 - 8*x^3 - 18*x^4 - x^5 + 11*x^6 + 12*x^7 + x^8). - Colin Barker, Mar 01 2019

Example

Some solutions for n=7:
..1..0..0..0..1..0..1. .0..0..0..0..1..1..1. .1..0..1..0..0..0..0
..1..1..0..0..1..1..1. .0..0..0..0..1..0..1. .0..1..0..0..0..1..0
..1..0..1..0..0..0..0. .0..1..1..0..0..0..0. .1..0..1..0..0..0..1

Crossrefs

Row 3 of A297582.

Sequence in context: A294952 A068810 A077115 * A073946 A016766 A242538

Adjacent sequences: A297581 A297582 A297583 * A297585 A297586 A297587

Keyword

nonn

Author

R. H. Hardin, Jan 01 2018

Status

approved