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A269215 Number of 2 X n 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three exactly once. 2

%I

%S 0,96,768,6528,49536,360960,2546304,17563392,119091072,796813824,

%T 5274483840,34608512256,225420724608,1459142258688,9394561013376,

%U 60205610853120,384263133750144,2443755614295552,15491594556534912

%N Number of 2 X n 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three exactly once.

%C Row 2 of A269214.

%H R. H. Hardin, <a href="/A269215/b269215.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 10*a(n-1) - 13*a(n-2) - 60*a(n-3) - 36*a(n-4).

%F G.f.: 96*x^2*(1 - x)^2 / ((1 + x)^2*(1 - 6*x)^2).

%F a(n) = 8*(175*6^n*n + 1008*n - 55*6^n - 288) / 1029 for n even.

%F a(n) = 8*(175*6^n*n - 1008*n - 55*6^n + 288) / 1029 for n odd.

%F (End)

%e Some solutions for n=4:

%e ..3..1..1..0. .3..2..2..2. .0..1..1..1. .2..0..2..0. .3..3..3..3

%e ..3..2..0..1. .2..0..2..0. .3..3..3..1. .1..2..2..2. .0..1..1..1

%Y Cf. A269214.

%K nonn

%O 1,2

%A _R. H. Hardin_, Feb 20 2016

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Last modified August 7 23:56 EDT 2020. Contains 336280 sequences. (Running on oeis4.)