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 A114295 #3 Nov 10 2007 03:00:00 %S A114295 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,1,5,5,5,5,5,2,1,13,13,13,13, %T A114295 13,5,2,1,34,34,34,34,34,13,5,2,1,89,89,89,89,89,34,13,5,2,1,288,288, %U A114295 288,288,288,110,42,16,6,2,1,1029,1029,1029,1029,1029,393,150,57,21,6,2,1 %N A114295 Modified Schroeder numbers for q=9. %C A114295 a(i,j) is the number of paths from (i,i) to (j,j) using steps of length (0,1), (1,0) and (1,1), not passing above the line y=x nor below the line y=4x/5. The Hamburger Theorem implies that we can use this table to calculate the number of domino tilings of an Aztec 9-pillow (A112842). To calculate this quantity, let P_n = the principal n X n submatrix of this array. If J_n = the back-diagonal matrix of order n, then A112842(n)=det(P_n+J_nP_n^(-1)J_n). %D A114295 C. Hanusa (2005). A Gessel-Viennot-Type Method for Cycle Systems with Applications to Aztec Pillows. PhD Thesis. University of Washington, Seattle, USA. %e A114295 The number of paths from (0,0) to (6,6) staying between the lines y=x and y=4x/5 using steps of length (0,1), (1,0) and (1,1) is a(0,6)=5. %Y A114295 See also A112833-A112844 and A114292-A114299. %K A114295 nonn,tabl %O A114295 0,16 %A A114295 Christopher Hanusa (chanusa(AT)math.binghamton.edu), Nov 21 2005