

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.


1



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

1,2


LINKS

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


FORMULA

Empirical: a(n) = 8*a(n1)  20*a(n2) + 32*a(n3)  84*a(n4) + 96*a(n5)  96*a(n6) + 128*a(n7)  64*a(n8) 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 A301586
Adjacent sequences: A281651 A281652 A281653 * A281655 A281656 A281657


KEYWORD

nonn


AUTHOR

R. H. Hardin, Jan 26 2017


STATUS

approved



