cp's OEIS Frontend

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.

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A083693 Sum of absolute values of list generated by n replacements of k by {-1-|k|, .., 1+|k|} with increment 2, starting with {1}.

Original entry on oeis.org

1, 4, 18, 72, 324, 1360, 6280, 27296, 128784, 573760, 2752032, 12485248, 60652608, 278988032, 1368979584, 6365514240, 31488733440, 147697177600, 735486927360, 3474529986560, 17398140748800, 82683153633280, 415966710171648
Offset: 0

Views

Author

Wouter Meeussen, May 03 2003

Keywords

Comments

Sum of absolute values of list elements starting from 0, (A083691), gives twice A083693, but with an initial zero.

Examples

			0, 1 and 2 substitutions produce lengths 1, 3 and 10:
{1}; {-2,0,2}; {-3,-1,1,3, -1,1, -3,-1,1,3} with sums of absolute values 1,4,18.
		

Crossrefs

Programs

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

Formula

A083691(n+2)/2-A083691(n+1)

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

Original entry on oeis.org

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

Views

Author

Wouter Meeussen, May 03 2003

Keywords

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.

Examples

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

Crossrefs

Programs

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

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)) ).
Showing 1-2 of 2 results.