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 A086114 #20 Dec 02 2024 16:31:06 %S A086114 8,64,216,528,1080,1968,3304,5216,7848,11360,15928,21744,29016,37968, %T A086114 48840,61888,77384,95616,116888,141520,169848,202224,239016,280608, %U A086114 327400,379808,438264,503216,575128,654480,741768,837504,942216,1056448 %N A086114 Number of 4 X n (0,1) matrices such that each row and each column is nondecreasing or nonincreasing. %H A086114 Don Coppersmith, <a href="https://research.ibm.com/haifa/ponderthis/challenges/March2004.html">Ponder This: IBM Research Monthly Puzzles, March 2004 challenge</a> %H A086114 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1). %F A086114 a(n) = (2/3)*n*(n^3+6*n^2+11*n-6). More generally, number of m X n (0, 1) matrices such that each row and each column is increasing or decreasing is 2*n*(2*binomial(n+m-1, n)-m) = 4/Beta(m, n)-2*m*n. %F A086114 G.f.: -8*x*(x^3-3*x^2+3*x+1) / (x-1)^5. [_Colin Barker_, Feb 22 2013] %Y A086114 Cf. A032260, A016742, A086113, A086115. %K A086114 nonn,easy %O A086114 1,1 %A A086114 _Vladimir Baltic_, _Vladeta Jovovic_, Jul 10 2003