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 A297395 #4 Dec 29 2017 10:56:51 %S A297395 1,2,1,3,5,1,4,9,9,1,6,13,19,20,1,9,33,37,57,41,1,13,69,127,126,139, %T A297395 85,1,19,121,323,700,385,369,178,1,28,253,763,2569,3175,1243,963,369, %U A297395 1,41,529,2121,7779,14940,15541,3924,2489,769,1,60,1013,5557,31081,58901,99682 %N A297395 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 neighboring 1. %C A297395 Table starts %C A297395 .1...2....3.....4.......6........9........13.........19...........28 %C A297395 .1...5....9....13......33.......69.......121........253..........529 %C A297395 .1...9...19....37.....127......323.......763.......2121.........5557 %C A297395 .1..20...57...126.....700.....2569......7779......31081.......117084 %C A297395 .1..41..139...385....3175....14940.....58901.....325922......1616869 %C A297395 .1..85..369..1243...15541....99682....514945....3977868.....27131403 %C A297395 .1.178..963..3924...74736...640562...4279111...46261441....428200086 %C A297395 .1.369.2489.12477..358341..4101278..35870939..540319235...6780786267 %C A297395 .1.769.6523.39625.1729617.26607999.302197213.6362528482.108762242579 %H A297395 R. H. Hardin, <a href="/A297395/b297395.txt">Table of n, a(n) for n = 1..420</a> %F A297395 Empirical for column k: %F A297395 k=1: a(n) = a(n-1) %F A297395 k=2: a(n) = a(n-1) +2*a(n-2) +a(n-3) -a(n-4) %F A297395 k=3: a(n) = a(n-1) +4*a(n-2) +2*a(n-3) -4*a(n-4) %F A297395 k=4: a(n) = a(n-1) +6*a(n-2) +4*a(n-3) -3*a(n-4) -a(n-5) -2*a(n-6) -a(n-7) %F A297395 k=5: [order 20] %F A297395 k=6: [order 25] %F A297395 k=7: [order 55] %F A297395 Empirical for row n: %F A297395 n=1: a(n) = a(n-1) +a(n-3) %F A297395 n=2: a(n) = a(n-1) +4*a(n-3) %F A297395 n=3: a(n) = a(n-1) +a(n-2) +8*a(n-3) +a(n-4) -2*a(n-6) %F A297395 n=4: [order 8] %F A297395 n=5: [order 21] %F A297395 n=6: [order 31] %F A297395 n=7: [order 69] %e A297395 Some solutions for n=5 k=4 %e A297395 ..0..0..1..1. .0..1..1..0. .0..1..0..0. .0..0..1..1. .0..0..0..0 %e A297395 ..0..0..0..0. .0..0..0..0. .1..0..0..0. .0..0..0..0. .0..0..1..0 %e A297395 ..0..1..1..0. .0..0..0..0. .0..0..0..0. .0..0..1..0. .0..0..0..1 %e A297395 ..0..0..0..0. .0..0..0..1. .0..0..0..0. .0..0..0..1. .0..1..0..0 %e A297395 ..0..0..1..1. .0..0..1..0. .1..1..0..0. .0..0..0..0. .1..0..0..0 %Y A297395 Column 2 is A105309(n+1). %Y A297395 Row 1 is A000930(n+1). %Y A297395 Row 2 is A089977(n+1). %K A297395 nonn,tabl %O A297395 1,2 %A A297395 _R. H. Hardin_, Dec 29 2017