%I #15 Sep 09 2019 02:27:58
%S 1,2,6,20,76,296,1240,5200,22960,100512,458592,2064704,9633472,
%T 44237440,209780096,977536256,4693031680,22117091840,107211650560,
%U 509817656320,2490609167360,11930278307840,58656838113280,282679983493120
%N Length of list generated by n replacements of k by {1k, ..., 1+k} with increment 2, starting with {0}.
%C 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. Crossreferences cite sequences with similar generation by integersubstitution and length of resulting lists.
%F G.f.: 1/x * series_reversion( (4*x5*x^2+x^2*sqrt(1+8*x+8*x^2))/ (2*(26*x6*x^22*x^3)) ).
%e 0, 1 and 2 substitutions produce lengths 1, 2 and 6: {0}; {1,1}; {2,0,2, 2,0,2}.
%t Table[Length@Flatten[Nest[ #/.k_Integer:>Table[i, {i, 1Abs[k], Abs[k]+1, 2}]&, {0}, w]], {w, 0, 10}]
%o (PARI) my(x='x+O('x^33)); Vec( serreverse( (4*x5*x^2+x^2*sqrt(1+8*x+8*x^2))/ (2*(26*x6*x^22*x^3)) ) ) \\ _Joerg Arndt_, Sep 09 2019
%Y Cf. A000108, A001003, A006319.
%Y Cf. A083692, A083693.
%K nonn
%O 0,2
%A _Wouter Meeussen_, May 03 2003
