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 A362153 #14 Apr 11 2023 13:26:00 %S A362153 1,8,29,73,151,276,463,729,1093,1576,2201,2993,3979,5188,6651,8401, %T A362153 10473,12904,15733,19001,22751,27028,31879,37353,43501,50376,58033, %U A362153 66529,75923,86276,97651,110113,123729,138568,154701,172201,191143,211604,233663,257401,282901,310248,339529 %N A362153 Number of skew shapes in a 3 X n rectangle with no empty rows or columns. %H A362153 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1). %F A362153 a(n) = (n^4 + 8*n^3 + 11*n^2 - 20*n + 12)/12. %F A362153 a(n) = [x^n] (-3*x^4 + 11*x^3 - 13*x^2 + 4*x - 1)/(x - 1)^5. - _Peter Luschny_, Apr 10 2023 %e A362153 The a(2) = 8 shapes are 211, 221, 222, 221/1, 222/1, 222/11, 221/11, 211/1. %p A362153 a := proc(n) m := n*(n + 4); m*(m - 5) / 12 + 1 end: %p A362153 seq(a(n), n = 1..43); # _Peter Luschny_, Apr 10 2023 %K A362153 nonn,easy %O A362153 1,2 %A A362153 _Richard Stanley_, Apr 09 2023