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 A224141 #7 Aug 27 2018 16:19:23 %S A224141 7,22,49,92,155,242,357,504,687,910,1177,1492,1859,2282,2765,3312, %T A224141 3927,4614,5377,6220,7147,8162,9269,10472,11775,13182,14697,16324, %U A224141 18067,19930,21917,24032,26279,28662,31185,33852,36667,39634,42757,46040,49487,53102 %N A224141 Number of n X 3 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing. %C A224141 Column 3 of A224146. %H A224141 R. H. Hardin, <a href="/A224141/b224141.txt">Table of n, a(n) for n = 1..210</a> %F A224141 Empirical: a(n) = (2/3)*n^3 + 2*n^2 + (13/3)*n. %F A224141 Conjectures from _Colin Barker_, Aug 27 2018: (Start) %F A224141 G.f.: x*(7 - 6*x + 3*x^2) / (1 - x)^4. %F A224141 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4. %F A224141 (End) %e A224141 Some solutions for n=3: %e A224141 ..0..0..0....0..0..0....0..1..1....0..1..0....0..0..1....0..1..0....0..0..1 %e A224141 ..0..0..0....0..0..0....1..1..1....0..1..1....0..0..1....0..1..0....1..1..1 %e A224141 ..0..0..1....1..1..1....1..1..1....1..1..1....0..1..1....0..1..0....1..1..1 %Y A224141 Cf. A224146. %K A224141 nonn %O A224141 1,1 %A A224141 _R. H. Hardin_, Mar 31 2013