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.

A200752 Expansion of (-x^2 + 3*x - 1)/(x^3 - x^2 + 3*x - 1).

Original entry on oeis.org

1, 0, 0, 1, 3, 8, 22, 61, 169, 468, 1296, 3589, 9939, 27524, 76222, 211081, 584545, 1618776, 4482864, 12414361, 34378995, 95205488, 263651830, 730128997, 2021940649, 5599344780, 15506222688, 42941263933, 118916913891, 329315700428, 911971451326, 2525515567441
Offset: 0

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Author

Alois P. Heinz, Nov 21 2011

Keywords

Comments

Peter A. Lawrence (see links) has posted a challenge to find a 3x3 integer matrix with "smallish" elements whose powers generate a sequence that is not in the OEIS. This sequence is one of the solutions found.
a(n+3) is the number of ternary strings of length n in which the number of substrings of the form 0011 equals the number of substrings of the form 11. - John M. Campbell, Nov 02 2013

Crossrefs

Programs

  • Maple
    a:= n-> (<<0|1|0>, <0|0|1>, <1|-1|3>>^n)[1, 1]:
    seq(a(n), n=0..50);

Formula

G.f.: (-x^2+3*x-1)/(x^3-x^2+3*x-1).
Term (1,1) in the 3x3 matrix [0,1,0; 0,0,1; 1,-1,3]^n.
a(n) = 3*a(n-1) -a(n-2) +a(n-3) with a(0)=1, a(1)=0, a(2)=0. - Taras Goy, Jul 23 2017