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

1, 2, 6, 20, 76, 296, 1240, 5200, 22960, 100512, 458592, 2064704, 9633472, 44237440, 209780096, 977536256, 4693031680, 22117091840, 107211650560, 509817656320, 2490609167360, 11930278307840, 58656838113280, 282679983493120

Offset

0,2

Comments

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.

Links

Table of n, a(n) for n=0..23.

Formula

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)) ).

Example

0, 1 and 2 substitutions produce lengths 1, 2 and 6: {0}; {-1,1}; {-2,0,2, -2,0,2}.

Mathematica

Table[Length@Flatten[Nest[ #/.k_Integer:>Table[i, {i, -1-Abs[k], Abs[k]+1, 2}]&, {0}, w]], {w, 0, 10}]

Prog

(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

Crossrefs

Cf. A000108, A001003, A006319.

Cf. A083692, A083693.

Sequence in context: A374569 A263901 A150169 * A150170 A150171 A263902

Adjacent sequences: A083688 A083689 A083690 * A083692 A083693 A083694

Keyword

nonn

Author

Wouter Meeussen, May 03 2003

Status

approved