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 A348008 #7 Oct 11 2021 18:55:53 %S A348008 1,3,7,19,45,115,273,683,1629,4035,9643,23713,56761,138883,332807, %T A348008 811343,1945777,4730655,11351999,27542291,66123953,160174529, %U A348008 384700337,930720767,2236106651,5404679299,12988762401,31370201873,75409375419,182019777165,437648513199 %N A348008 Number of n-step self-avoiding walks on the upper two quadrants of a 2D square lattice where the walk cannot step to the smaller square ring of numbers than the ring it is currently on. %C A348008 This is a variation of A347990. The same walk rules apply except that the walk is confined to the upper two quadrants of the 2D square lattice. See A347990 for further details. %e A348008 a(0..3) are the same as the standard SAW on the upper two quadrants of a square lattice, see A116903, as the walk cannot step to a smaller ring in the first three steps. %e A348008 a(4) = 45. If we restrict the first one or more steps to the right followed by an upward step then there is one walk which steps to a smaller ring and is thus forbidden. That is the walk (0,0) -> (1,0) -> (2,0) -> (2,1) -> (1,1). As this can be walked in four different ways in the upper two quadrants the number of 4-step walks becomes A116903(4) - 4 = 49 - 4 = 45. %Y A348008 Cf. A347990 (four quadrants), A348009 (one quadrant), A116903, A001411, A337353. %K A348008 nonn,walk %O A348008 0,2 %A A348008 _Scott R. Shannon_, Sep 24 2021