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.

A189800 a(n) = 6*a(n-1) + 8*a(n-2), with a(0)=0, a(1)=1.

Original entry on oeis.org

0, 1, 6, 44, 312, 2224, 15840, 112832, 803712, 5724928, 40779264, 290475008, 2069084160, 14738305024, 104982503424, 747801460736, 5326668791808, 37942424436736, 270267896954880, 1925146777223168, 13713023838978048, 97679317251653632, 695780094221746176
Offset: 0

Views

Author

Vladimir Joseph Stephan Orlovsky, May 24 2011

Keywords

Links

Crossrefs

Sequences of the form a(n) = c*a(n-1) + d*a(n-2), with a(0)=0, a(1)=1:
c/d...1.......2.......3.......4.......5.......6.......7.......8.......9......10
1..A000045,A001045,A006130,A006131,A015440,A015441,A015442,A015443,A015445,A015446
2..A000129,A002605,A015518,A063727,A002532,A083099,A015519,A003683,A002534,A083102
3..A006190,A007482,A030195,A015521,A015523,A083858,A015524,A015525,A099012,A015528
4..A001076,A090017,A015530,A057087,A015531,A085939,A015532,A180222,A015533,A180226
5..A052918,A015535,A015536,A015537,A057088,A015540,A015541,A015544,A015545,A180250
6..A005668,A135030,A090018,A135032,A015551,A057089,A015552,A189800,A189801,A190005
7..A054413,A015555,A015559,A015561,A015562,A015564,A057090,A015565,A015566,A015568
8..A041025,A190331,A015574,A190510,A015575,A190560,A015576,A057091,A015577,A190953
9..A099371,A015579,A181353,A015580,A015581,A153191,A015583,A015584,A057092,A015585
10.A041041,A191014,A015588,A190954,A190955,A190956,A015589,A190957,A015591,A057093

Programs

  • Magma
    I:=[0,1]; [n le 2 select I[n] else 6*Self(n-1)+8*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 14 2011
  • Mathematica
    LinearRecurrence[{6, 8}, {0, 1}, 50]
CoefficientList[Series[-(x/(-1+6 x+8 x^2)),{x,0,50}],x] (* Harvey P. Dale, Jul 26 2011 *)
  • PARI
    a(n)=([0,1; 8,6]^n*[0;1])[1,1] \\ Charles R Greathouse IV, Oct 03 2016

Formula

G.f.: x/(1 - 2*x*(3+4*x)). - Harvey P. Dale, Jul 26 2011

A254599 Numbers of words on alphabet {0,1,...,9} with no subwords ii, for i from {0,1}.

Original entry on oeis.org

1, 10, 98, 962, 9442, 92674, 909602, 8927810, 87627106, 860066434, 8441614754, 82855064258, 813228496354, 7981896981250, 78342900802082, 768941283068738, 7547214754035298, 74076463050867586, 727065885490090658, 7136204673817756610, 70042369148280534754
Offset: 0

Views

Author

Milan Janjic, Feb 02 2015

Keywords

Comments

a(n) is the number of sequences over {0,1,...,9} of length n such that no two consecutive terms have distance 9. - David Nacin, May 31 2017

Links

Crossrefs

Cf. A015584, A055099, A126473, A126501, A126528.

Programs

  • Magma
    [n le 1 select 10^n else 9*Self(n)+8*Self(n-1): n in [0..20]]; // Bruno Berselli, Feb 02 2015
  • Mathematica
    RecurrenceTable[{a[0] == 1, a[1] == 10, a[n] == 9 a[n - 1] + 8 a[n - 2]}, a[n], {n, 0, 20}] (* Bruno Berselli, Feb 02 2015 *)
  • PARI
    Vec((1 + x)/(1 - 9*x - 8*x^2) + O(x^30)) \\ Colin Barker, Jan 22 2017

Formula

a(n) = 9*a(n-1) + 8*a(n-2) with n>1, a(0) = 1, a(1) = 10.
G.f.: (1 + x)/(1 - 9*x - 8*x^2). - Bruno Berselli, Feb 02 2015
a(n) = (2^(-1-n)*((9-r)^n*(-11+r) + (9+r)^n*(11+r))) / r, where r=sqrt(113). - Colin Barker, Jan 22 2017
Showing 1-2 of 2 results.

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