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 A194773 #12 May 05 2018 13:18:01 %S A194773 43,105,265,655,1641,4069,10121,25025,61809,152019,372979,912017, %T A194773 2224175,5408825,13120905,31752431,76673045,184762437,444388957, %U A194773 1066954113,2557518625,6121119363,14629468735,34918297649,83242029523,198212839881 %N A194773 Number of lower triangles of an (n+4) X (n+4) 0..3 array with new values introduced in row major order 0..3 and no element unequal to more than one horizontal or vertical neighbor. %C A194773 Column 3 of A194778. %H A194773 R. H. Hardin, <a href="/A194773/b194773.txt">Table of n, a(n) for n = 1..27</a> %F A194773 Empirical: a(n) = 5*a(n-1) -2*a(n-2) -22*a(n-3) +21*a(n-4) +35*a(n-5) -34*a(n-6) -26*a(n-7) +15*a(n-8) +9*a(n-9). %F A194773 Empirical g.f.: x*(43 - 110*x - 174*x^2 + 486*x^3 + 303*x^4 - 706*x^5 - 310*x^6 + 318*x^7 + 153*x^8) / ((1 - x)*(1 - x - x^2)^2*(1 - x - 3*x^2)^2). - _Colin Barker_, May 05 2018 %e A194773 All solutions for 5 X 5 including a 3: %e A194773 0 0 %e A194773 1 1 1 1 %e A194773 1 1 2 1 1 1 %e A194773 1 1 2 2 2 2 2 2 %e A194773 1 1 2 2 3 2 2 2 2 3 %Y A194773 Cf. A194778. %K A194773 nonn %O A194773 1,1 %A A194773 _R. H. Hardin_, Sep 02 2011