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 A359741 #16 Jan 15 2023 15:11:26 %S A359741 1,6,6,30,78,1134,1350,20574,23238,390606,496998,7614750,10987926, %T A359741 152120934,237122526,3110708214,5017927638,64718847438,105210653478, %U A359741 1362453235998 %N A359741 Number of n-step self-avoiding walks on a 3D cubic lattice whose end-to-end distance is an integer. %C A359741 The walks counted are all those directly along and x, y or z axes, and all walks whose final (x,y,z) lattice point is a solution to the Pythagorean quadruple x^2 + y^2 + z^2 = t^2. The first such solution with all coordinates > 0 is 1^2 + 2^2 + 2^2 = 3^2, which explains the large increase in the number of walks from a(4) to a(5). %H A359741 Wikipedia, <a href="https://en.wikipedia.org/wiki/Self-avoiding_walk">Self-avoiding walk</a>. %H A359741 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pythagorean_quadruple">Pythagorean quadruple</a>. %e A359741 a(3) = 30 as, in the first octant, there is one 3-step SAW whose end-to-end distance is an integer (1 unit): %e A359741 . %e A359741 X---. %e A359741 | %e A359741 X---. %e A359741 . %e A359741 This can be walked in 24 different ways on a 3D cubic lattice. There are also the six walks directly along the x, y and z axes, giving a total of 24 + 6 = 30 walks. %Y A359741 Cf. A359133, A001412, A359709, A118313. %K A359741 nonn,walk,more %O A359741 0,2 %A A359741 _Scott R. Shannon_, Jan 12 2023