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A083691 Length of list generated by n replacements of k by {-1-|k|, ..., 1+|k|} with increment 2, starting with {0}. 2

%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 {-1-|k|, ..., 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. Cross-references cite sequences with similar generation by integer-substitution and length of resulting lists.

%F 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 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, -1-Abs[k], Abs[k]+1, 2}]&, {0}, w]], {w, 0, 10}]

%o (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 Cf. A000108, A001003, A006319.

%Y Cf. A083692, A083693.

%K nonn

%O 0,2

%A _Wouter Meeussen_, May 03 2003

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Last modified May 25 16:13 EDT 2024. Contains 372800 sequences. (Running on oeis4.)