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 A195000 #9 May 06 2018 10:12:14 %S A195000 2,80,248,458,672,888,1104,1320,1536,1752,1968,2184,2400,2616,2832, %T A195000 3048,3264,3480,3696,3912,4128,4344,4560,4776,4992,5208,5424,5640, %U A195000 5856,6072,6288,6504,6720,6936,7152,7368,7584,7800,8016,8232,8448,8664,8880,9096 %N A195000 Number of lower triangles of a 4 X 4 0..n array with each element differing from all of its horizontal and vertical neighbors by one. %C A195000 Row 4 of A194998. %H A195000 R. H. Hardin, <a href="/A195000/b195000.txt">Table of n, a(n) for n = 1..200</a> %F A195000 Conjectures from _Colin Barker_, May 06 2018: (Start) %F A195000 G.f.: 2*x*(1 + 38*x + 45*x^2 + 21*x^3 + 2*x^4 + x^5) / (1 - x)^2. %F A195000 a(n) = 24*(9*n - 17) for n>4. %F A195000 a(n) = 2*a(n-1) - a(n-2) for n>6. %F A195000 (End) %e A195000 Some solutions for n=4: %e A195000 ..1........4........3........4........2........1........1........0 %e A195000 ..2.1......3.2......2.3......3.2......3.4......0.1......2.1......1.2 %e A195000 ..1.0.1....2.1.2....3.4.3....2.1.2....2.3.4....1.2.1....3.2.3....2.3.2 %e A195000 ..0.1.0.1..1.2.3.4..2.3.2.1..1.0.1.0..3.4.3.2..2.1.2.1..2.3.2.3..3.2.1.0 %Y A195000 Cf. A194998. %K A195000 nonn %O A195000 1,1 %A A195000 _R. H. Hardin_, Sep 07 2011