The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

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