A268768 Number of n X 2 0..2 arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

3, 12, 32, 100, 248, 620, 1456, 3380, 7656, 17148, 37920, 83140, 180824, 390796, 839824, 1796180, 3825352, 8116764, 17165568, 36195300, 76118840, 159694252, 334301552, 698429300, 1456510888, 3032326460, 6303262176, 13083742980

Offset

1,1

Links

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

Formula

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

Conjectures from Colin Barker, Jan 14 2019: (Start)

G.f.: x*(3 + 6*x - x^2 + 12*x^3 + 12*x^4) / ((1 + x)^2*(1 - 2*x)^2).

a(n) = (4/27)*(7*((-1)^n-2^n) + 3*((-1)^n + 2^(2+n))*n) for n>1.

(End)

Example

Some solutions for n=4:
..1..2. .0..1. .2..1. .0..1. .1..0. .2..1. .0..1. .1..1. .0..0. .2..1
..2..2. .0..0. .2..2. .1..0. .0..1. .2..2. .0..0. .2..2. .0..0. .1..2
..1..1. .1..0. .2..1. .0..0. .0..0. .1..2. .0..0. .2..2. .0..1. .2..2
..0..0. .0..1. .1..2. .1..0. .0..1. .1..2. .1..1. .1..2. .1..0. .2..1

Crossrefs

Column 2 of A268774.

Sequence in context: A309693 A365738 A288605 * A174963 A054602 A083725

Adjacent sequences: A268765 A268766 A268767 * A268769 A268770 A268771

Keyword

nonn

Author

R. H. Hardin, Feb 13 2016

Status

approved