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 A114294 #3 Nov 10 2007 03:00:00 %S A114294 1,1,1,1,1,1,1,1,1,1,2,2,2,2,1,5,5,5,5,2,1,13,13,13,13,5,2,1,34,34,34, %T A114294 34,13,5,2,1,110,110,110,110,42,16,6,2,1,393,393,393,393,150,57,21,6, %U A114294 2,1,1449,1449,1449,1449,553,210,77,21,6,2,1,5390,5390,5390,5390,2057,781 %N A114294 Modified Schroeder numbers for q=7. %C A114294 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=3x/4. The Hamburger Theorem implies that we can use this table to calculate the number of domino tilings of an Aztec 7-pillow (A112839). 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 A112839(n)=det(P_n+J_nP_n^(-1)J_n). %D A114294 C. Hanusa (2005). A Gessel-Viennot-Type Method for Cycle Systems with Applications to Aztec Pillows. PhD Thesis. University of Washington, Seattle, USA. %e A114294 The number of paths from (0,0) to (5,5) staying between the lines y=x and y=3x/4 using steps of length (0,1), (1,0) and (1,1) is a(0,5)=5. %Y A114294 See also A112833-A112844 and A114292-A114299. %K A114294 nonn,tabl %O A114294 0,11 %A A114294 Christopher Hanusa (chanusa(AT)math.binghamton.edu), Nov 21 2005