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A232670 Number of (n+1) X (1+1) 0..2 arrays with every element next to itself plus and minus one within the range 0..2 horizontally, vertically, diagonally or antidiagonally. 1

%I

%S 36,212,1568,11878,87680,651678,4846056,35990386,267429284,1987124934,

%T 14763908592,109698051138,815067420300,6055993810126,44996556671640,

%U 334327945984154,2484081968889732,18456924487924070,137136383652862288

%N Number of (n+1) X (1+1) 0..2 arrays with every element next to itself plus and minus one within the range 0..2 horizontally, vertically, diagonally or antidiagonally.

%H R. H. Hardin, <a href="/A232670/b232670.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 21*a(n-2) + 118*a(n-3) + 170*a(n-4) + 166*a(n-5) - 52*a(n-6) - 48*a(n-7) - 64*a(n-8).

%F Empirical g.f.: 2*x*(18 + 70*x + 194*x^2 + 21*x^3 - 70*x^4 - 80*x^5 - 32*x^6) / (1 - 2*x - 21*x^2 - 118*x^3 - 170*x^4 - 166*x^5 + 52*x^6 + 48*x^7 + 64*x^8). - _Colin Barker_, Oct 05 2018

%e Some solutions for n=5:

%e ..2..1....0..2....2..1....1..2....0..2....2..1....1..2....1..2....0..2....0..1

%e ..1..0....0..1....1..0....1..0....1..0....1..0....2..0....0..1....1..2....2..1

%e ..2..0....2..0....2..0....1..0....2..2....0..0....0..0....0..0....2..1....1..1

%e ..0..2....2..0....2..1....0..2....2..1....2..1....1..0....2..1....0..1....0..2

%e ..0..1....1..0....2..0....0..2....0..1....2..0....1..2....0..1....1..1....1..2

%e ..2..2....0..2....2..1....0..1....2..2....1..0....2..0....1..2....2..2....2..0

%Y Column 1 of A232677.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 27 2013

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Last modified October 1 14:19 EDT 2022. Contains 357149 sequences. (Running on oeis4.)