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 A083691 #15 Sep 09 2019 02:27:58
%S A083691 1,2,6,20,76,296,1240,5200,22960,100512,458592,2064704,9633472,
%T A083691 44237440,209780096,977536256,4693031680,22117091840,107211650560,
%U A083691 509817656320,2490609167360,11930278307840,58656838113280,282679983493120
%N A083691 Length of list generated by n replacements of k by {-1-|k|, ..., 1+|k|} with increment 2, starting with {0}.
%C A083691 G.f. from SuperSeeker (LISTTOALGEQ) checked up to n=11. Same sequence starting with {1}: see A083692. Sum of absolute values of list elements gives A083693. Cross-references cite sequences with similar generation by integer-substitution and length of resulting lists.
%F A083691 G.f.: 1/x * series_reversion( (-4*x-5*x^2+x^2*sqrt(1+8*x+8*x^2))/ (2*(-2-6*x-6*x^2-2*x^3)) ).
%e A083691 0, 1 and 2 substitutions produce lengths 1, 2 and 6: {0}; {-1,1}; {-2,0,2, -2,0,2}.
%t A083691 Table[Length@Flatten[Nest[ #/.k_Integer:>Table[i, {i, -1-Abs[k], Abs[k]+1, 2}]&, {0}, w]], {w, 0, 10}]
%o A083691 (PARI) my(x='x+O('x^33)); Vec( serreverse( (-4*x-5*x^2+x^2*sqrt(1+8*x+8*x^2))/ (2*(-2-6*x-6*x^2-2*x^3)) ) ) \\ _Joerg Arndt_, Sep 09 2019
%Y A083691 Cf. A000108, A001003, A006319.
%Y A083691 Cf. A083692, A083693.
%K A083691 nonn
%O A083691 0,2
%A A083691 _Wouter Meeussen_, May 03 2003