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.

Showing 1-2 of 2 results.

A015585 a(n) = 9*a(n-1) + 10*a(n-2).

Original entry on oeis.org

0, 1, 9, 91, 909, 9091, 90909, 909091, 9090909, 90909091, 909090909, 9090909091, 90909090909, 909090909091, 9090909090909, 90909090909091, 909090909090909, 9090909090909091, 90909090909090909, 909090909090909091, 9090909090909090909, 90909090909090909091
Offset: 0

Views

Author

Olivier Gérard

Keywords

Comments

Number of walks of length n between any two distinct nodes of the complete graph K_11. Example: a(2)=9 because the walks of length 2 between the nodes A and B of the complete graph ABCDEFGHIJK are: ACB, ADB, AEB, AFB, AGB, AHB, AIB, AJB and AKB. - Emeric Deutsch, Apr 01 2004
Beginning with n=1 and a(1)=1, these are the positive integers whose balanced base-10 representations (A097150) are the first n digits of 1,-1,1,-1,.... Also, a(n) = (-1)^(n-1)*A014992(n) = |A014992(n)| for n >= 1. - Rick L. Shepherd, Jul 30 2004
General form: k=10^n-k. Also: A001045, A078008, A097073, A115341, A015518, A054878, A015521, A109499, A015531, A109500, A109501, A015552, A093134, A015565, A015577. - Vladimir Joseph Stephan Orlovsky, Dec 11 2008

Links

Crossrefs

Cf. A014992 (q-integers for q=-10), A097150.
Cf. A001045, A078008, A097073, A115341, A015518, A054878, A015521, A109499, A015531, A109500, A109501, A015552, A093134, A015565, A015577. - Vladimir Joseph Stephan Orlovsky, Dec 11 2008
Cf. A094028, A098610, A098611.

Programs

Formula

a(n) = 9*a(n-1) + 10*a(n-2).
From Emeric Deutsch, Apr 01 2004: (Start)
a(n) = 10^(n-1) - a(n-1).
G.f.: x/(1 - 9x - 10x^2). (End)
From Henry Bottomley, Sep 17 2004: (Start)
a(n) = round(10^n/11).
a(n) = (10^n - (-1)^n)/11.
a(n) = A098611(n)/11 = 9*A094028(n+1)/A098610(n). (End)
E.g.f.: exp(-x)*(exp(11*x) - 1)/11. - Elmo R. Oliveira, Aug 17 2024

Extensions

Extended by T. D. Noe, May 23 2011

A098611 a(n) = 10^n - (-1)^n.

Original entry on oeis.org

0, 11, 99, 1001, 9999, 100001, 999999, 10000001, 99999999, 1000000001, 9999999999, 100000000001, 999999999999, 10000000000001, 99999999999999, 1000000000000001, 9999999999999999, 100000000000000001, 999999999999999999, 10000000000000000001
Offset: 0

Views

Author

Henry Bottomley, Sep 17 2004

Keywords

Links

Crossrefs

Cf. A015585, A098609, A098610.

Programs

  • Magma
    [10^n-(-1)^n : n in [0..30]]; // Wesley Ivan Hurt, Apr 05 2015
  • Maple
    A098611:=n->10^n-(-1)^n: seq(A098611(n), n=0..30); # Wesley Ivan Hurt, Apr 05 2015
  • Mathematica
    Table[(10^n - (-1)^n), {n, 0, 30}] (* or *)
CoefficientList[Series[11 x/(1 - 9 x - 10 x^2), {x, 0, 30}], x] (* Wesley Ivan Hurt, Apr 05 2015 *)
LinearRecurrence[{9, 10}, {0, 11}, 20] (* Vincenzo Librandi, Apr 06 2015 *)
  • PARI
    vector(20,n, 10^(n-1)+(-1)^n) \\ Derek Orr, Apr 05 2015

Formula

a(n) = A098610(n) - 2*(-1)^n = A098609(n)/A098610(n).
From Wesley Ivan Hurt, Apr 05 2015: (Start)
G.f.: 11*x/(1-9*x-10*x^2).
a(n) = 9*a(n-1) + 10*a(n-2). (End)
From Elmo R. Oliveira, Aug 17 2024: (Start)
E.g.f.: exp(-x)*(exp(11*x) - 1).
a(n) = 11*A015585(n). (End)
Showing 1-2 of 2 results.

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