A281654 Number of 2 X n 0..2 arrays with no element equal to more than one of its horizontal, diagonal or antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 4, 70, 400, 2128, 10512, 49352, 225024, 1003104, 4395200, 19006304, 81319168, 344886784, 1452055808, 6075680384, 25286555648, 104754555392, 432208419840, 1776869555712, 7281672187904, 29755307585536, 121277018935296

Offset

1,2

Links

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

Formula

Empirical: a(n) = 8*a(n-1) - 20*a(n-2) + 32*a(n-3) - 84*a(n-4) + 96*a(n-5) - 96*a(n-6) + 128*a(n-7) - 64*a(n-8) for n>9.

Empirical g.f.: 2*x^2*(2 + 19*x - 40*x^2 + 100*x^3 - 208*x^4 + 256*x^5 - 192*x^6 + 64*x^7) / (1 - 4*x + 2*x^2 - 8*x^3 + 8*x^4)^2. - Colin Barker, Feb 20 2019

Example

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

Crossrefs

Row 2 of A281653.

Sequence in context: A278553 A101841 A274873 * A222309 A061609 A349457

Adjacent sequences: A281651 A281652 A281653 * A281655 A281656 A281657

Keyword

nonn

Author

R. H. Hardin, Jan 26 2017

Status

approved