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 A374300 #15 Jul 26 2024 14:02:21
%S A374300 5,44,330,2231,14234,87670,526549,3105097,18061476,103955447,
%T A374300 593388315,3364743202,18977238539,106562551704,596209056866,
%U A374300 3325672377580,18503794814297,102734584002260,569364274759972,3150649232873918,17411856639412771,96118767225465184
%N A374300 Number of growing self-avoiding walks with displacement n on a half-infinite strip of height 4 with a trapped endpoint.
%C A374300 A growing self-avoiding walk (GSAW) is a walk on a graph that is directed, does not visit the same vertex twice, and for which all neighbors of the endpoint are part of the walk, i.e., the endpoint is trapped. This sequence is about GSAWs on the grid graph of integer points (x,y) where x >= 0 and y is in {0,1,2,3}. The GSAW must start at the point (0,0). The displacement of a GSAW is the difference between the largest and smallext x-values that it reaches.
%H A374300 Jay Pantone, A. R. Klotz, and E. Sullivan, <a href="https://arxiv.org/abs/2407.18205">Exactly-solvable self-trapping lattice walks. II. Lattices of arbitrary height.</a>, arXiv:2407.18205 [math.CO], 2024.
%F A374300 G.f.: (-(11*x^12+4*x^11-138*x^10+205*x^9+119*x^8-552*x^7+485*x^6-93*x^5-112*x^4+132*x^3-85*x^2+31*x-5)*x)/((x^6+2*x^5-9*x^4-5*x^3+15*x^2-8*x+1)*(2*x^5+3*x^4-7*x^3+12*x^2-7*x+1)).
%e A374300 The a(1) = 5 walks are:
%e A374300 *--* * *--* * *--* * * * * *--* *
%e A374300 | | | | | |
%e A374300 *--* * * * * *--* * *--* * * * *
%e A374300 | | | | | | |
%e A374300 * * * *--* * *--* * * * * * * *
%e A374300 | | | | |
%e A374300 * * * * * * *--* * *--* * *--* *
%Y A374300 Cf. A078528, A374299.
%K A374300 nonn,easy
%O A374300 1,1
%A A374300 _Jay Pantone_, Jul 16 2024