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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

A098610 a(n) = 10^n + (-1)^n.

Original entry on oeis.org

2, 9, 101, 999, 10001, 99999, 1000001, 9999999, 100000001, 999999999, 10000000001, 99999999999, 1000000000001, 9999999999999, 100000000000001, 999999999999999, 10000000000000001, 99999999999999999, 1000000000000000001, 9999999999999999999, 100000000000000000001
Offset: 0

Views

Author

Henry Bottomley, Sep 17 2004

Keywords

Links

Crossrefs

Cf. A015585, A094028, A098609, A098611.

Programs

  • Magma
    [10^n+(-1)^n: n in [0..20]]; // Vincenzo Librandi, Sep 23 2016
  • Mathematica
    Total/@Partition[Riffle[10^Range[0,20],{1,-1}],2] (* or *) Table[10^n+(-1)^n,{n,0,20}] (* Harvey P. Dale, Aug 20 2012 *)

Formula

a(n) = A098611(n) + 2*(-1)^n.
a(n) = A098609(n)/A098611(n).
a(n) = A098609(n)/(11*A015585(n)).
a(n) = 9*A094028(n+1)/A015585(n).
From Chai Wah Wu, Sep 22 2016: (Start)
a(n) = 9*a(n-1) + 10*a(n-2) for n > 1.
G.f.: (9*x - 2)/((x + 1)*(10*x - 1)). (End)
E.g.f.: exp(-x)*(exp(11*x) + 1). - Elmo R. Oliveira, Aug 17 2024
Showing 1-2 of 2 results.

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