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 A247943 #19 Nov 04 2014 16:40:03 %S A247943 0,2,2,6,60,6,12,1058,1058,12,20,25080,140240,25080,20,30,822594, %T A247943 58673472,58673472,822594,30,42,36195620,28938943114,490225231968, %U A247943 28938943114,36195620,42,56,2069486450 %N A247943 2-dimensional array T(n, k) listed by antidiagonals giving the number of acyclic paths in the graph G(n, k) whose vertices are the integer lattice points (p, q) with 0 <= p < n and 0 <= q < k and with an edge between v and w iff the line segment [v, w] contains no other integer lattice points. %C A247943 There is an edge between v = (p, q) and w = (r, s) iff p - r and q - s are coprime. %C A247943 G(3, 3) is used for Android screen lock security patterns (see StackExchange link). %C A247943 The nonzero entries on the diagonal of this sequence comprise the row sums of A247944. %H A247943 StackExchange, <a href="http://math.stackexchange.com/questions/37167/combination-of-smartphones-pattern-password">Combination of smartphones' pattern password</a>, 2014 %e A247943 G(2,2) is the complete graph on 4 vertices, hence T(2, 2) = 4*3 + 4*3*2 + 4*3*2*1 = 60. %e A247943 T(n, k) for n + k <= 8 is as follows: %e A247943 .0........2...........6...........12..........20.......30..42 %e A247943 .2.......60........1058........25080......822594.36195620 %e A247943 .6.....1058......140240.....58673472.28938943114 %e A247943 12....25080....58673472.490225231968 %e A247943 20...822594.28938943114 %e A247943 30.36195620 %e A247943 42 %Y A247943 Cf. A247944. %K A247943 nonn,tabl %O A247943 1,2 %A A247943 _Rob Arthan_, Sep 27 2014