This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A269215 #9 Apr 25 2024 09:32:20 %S A269215 0,96,768,6528,49536,360960,2546304,17563392,119091072,796813824, %T A269215 5274483840,34608512256,225420724608,1459142258688,9394561013376, %U A269215 60205610853120,384263133750144,2443755614295552,15491594556534912 %N A269215 Number of 2 X n 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three exactly once. %C A269215 Row 2 of A269214. %H A269215 R. H. Hardin, <a href="/A269215/b269215.txt">Table of n, a(n) for n = 1..210</a> %F A269215 Empirical: a(n) = 10*a(n-1) - 13*a(n-2) - 60*a(n-3) - 36*a(n-4). %F A269215 From _Colin Barker_, Mar 21 2018: (Start) %F A269215 G.f.: 96*x^2*(1 - x)^2 / ((1 + x)^2*(1 - 6*x)^2). %F A269215 a(n) = 8*(175*6^n*n + 1008*n - 55*6^n - 288) / 1029 for n even. %F A269215 a(n) = 8*(175*6^n*n - 1008*n - 55*6^n + 288) / 1029 for n odd. %F A269215 (End) %e A269215 Some solutions for n=4: %e A269215 ..3..1..1..0. .3..2..2..2. .0..1..1..1. .2..0..2..0. .3..3..3..3 %e A269215 ..3..2..0..1. .2..0..2..0. .3..3..3..1. .1..2..2..2. .0..1..1..1 %Y A269215 Cf. A269214. %K A269215 nonn %O A269215 1,2 %A A269215 _R. H. Hardin_, Feb 20 2016