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 A302212 #4 Apr 03 2018 12:01:55 %S A302212 1,1,2,1,2,4,1,11,2,8,1,13,16,3,16,1,34,5,47,6,32,1,65,32,7,147,10,64, %T A302212 1,123,22,111,18,386,21,128,1,266,72,80,448,55,1065,42,256,1,499,101, %U A302212 424,281,1725,172,3063,86,512,1,1037,216,1157,1868,1395,6423,575,8624,179 %N A302212 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero. %C A302212 Table starts %C A302212 ...1..1....1....1.....1......1.......1........1........1..........1...........1 %C A302212 ...2..2...11...13....34.....65.....123......266......499.......1037........2042 %C A302212 ...4..2...16....5....32.....22......72......101......216........486.........968 %C A302212 ...8..3...47....7...111.....80.....424.....1157.....2922......12816.......33744 %C A302212 ..16..6..147...18...448....281....1868.....6036....16344.....110672......332791 %C A302212 ..32.10..386...55..1725...1395...11170....46215...142804....1296927.....3754619 %C A302212 ..64.21.1065..172..6423...8756...55922...465040..1136003...19265064....60547641 %C A302212 .128.42.3063..575.24927..43128..291320..3509969..9080114..212347228...786789878 %C A302212 .256.86.8624.1962.96909.234170.1544411.29343177.73189971.2698247985.11028726211 %H A302212 R. H. Hardin, <a href="/A302212/b302212.txt">Table of n, a(n) for n = 1..240</a> %F A302212 Empirical for column k: %F A302212 k=1: a(n) = 2*a(n-1) %F A302212 k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5) %F A302212 k=3: [order 9] %F A302212 k=4: [order 28] for n>32 %F A302212 k=5: [order 37] for n>41 %F A302212 Empirical for row n: %F A302212 n=1: a(n) = a(n-1) %F A302212 n=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5 %F A302212 n=3: [order 19] for n>20 %F A302212 n=4: [order 61] for n>62 %e A302212 Some solutions for n=5 k=4 %e A302212 ..0..1..0..0. .0..1..0..0. .0..0..1..0. .0..1..0..0. .0..0..1..1 %e A302212 ..0..1..0..0. .0..1..0..0. .0..0..1..0. .0..1..0..0. .0..0..1..1 %e A302212 ..1..1..1..0. .1..1..1..1. .1..1..1..1. .0..1..0..1. .0..1..1..0 %e A302212 ..0..1..0..0. .0..0..1..0. .0..1..0..0. .0..1..0..0. .0..0..1..1 %e A302212 ..0..1..0..0. .0..0..1..0. .0..1..0..0. .0..1..0..0. .0..0..1..1 %Y A302212 Column 1 is A000079(n-1). %Y A302212 Column 2 is A240513(n-2). %Y A302212 Row 2 is A297870(n+2). %K A302212 nonn,tabl %O A302212 1,3 %A A302212 _R. H. Hardin_, Apr 03 2018