Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #9 Apr 25 2024 09:32:20
%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 From _Colin Barker_, Mar 21 2018: (Start)
%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