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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A083426 a(n) = (4*7^n+2^n)/5.

Original entry on oeis.org

1, 6, 40, 276, 1924, 13452, 94132, 658860, 4611892, 32282988, 225980404, 1581861804, 11073030580, 77511209964, 542578461556, 3798049214508, 26586344468788, 186104411215980, 1302730878380788, 9119116148403372
Offset: 0

Views

Author

Paul Barry, Apr 30 2003

Keywords

Comments

Binomial transform of A083066.

Links

Crossrefs

Cf. A083066.

Programs

  • Mathematica
    LinearRecurrence[{9,-14},{1,6},20] (* Harvey P. Dale, Oct 13 2015 *)

Formula

G.f.: (1-3*x)/((1-2*x)*(1-7*x)).
E.g.f.: (4*exp(7*x)+exp(2*x))/5.

A086713 A squarefree sequence: define a mapping from the set of strings over the alphabet {0,1,2} by f(0)=01201, f(1)=020121, f(2)=0212021 and f of the concatenation of s and t is the concatenation of f(s) and f(t). Then each of 0, f(0), f(f(0)), ... is an initial substring of the next; their limit is the infinite sequence given above.

Original entry on oeis.org

0, 1, 2, 0, 1, 0, 2, 0, 1, 2, 1, 0, 2, 1, 2, 0, 2, 1, 0, 1, 2, 0, 1, 0, 2, 0, 1, 2, 1, 0, 1, 2, 0, 1, 0, 2, 1, 2, 0, 2, 1, 0, 1, 2, 0, 1, 0, 2, 0, 1, 2, 1, 0, 2, 1, 2, 0, 2, 1, 0, 2, 0, 1, 2, 1, 0, 1, 2, 0, 1, 0, 2, 1, 2, 0, 2, 1, 0, 2, 0, 1, 2, 1, 0, 2, 1, 2, 0, 2, 1, 0, 1, 2, 0, 1, 0, 2, 1, 2, 0, 2, 1, 0, 2, 0
Offset: 0

Views

Author

Claude Lenormand (claude.lenormand(AT)free.fr), Jul 29 2003

Keywords

Comments

f is a "squarefree morphism"; i.e. f(s) is squarefree iff s is squarefree.
For any i>0, f^i(0) has the same number of 0's and 1's and one less 2. The length of f^i(0) is A083066(i) = (4*6^i + 1)/5.

Examples

			f(f(0))=01201020121021202101201020121

References

  • Jean Berstel and Christophe Reutenauer, Squarefree words, p. 31.
  • M. Lothaire, Combinatorics on Words, Cambridge University Press, 1997.

Programs

  • Mathematica
    f[s_] := Flatten[{{0, 1, 2, 0, 1}, {0, 2, 0, 1, 2, 1}, {0, 2, 1, 2, 0, 2, 1}}[[ #+1]]&/@s]; f[f[f[{0}]]]

Extensions

Edited by Dean Hickerson, Oct 19 2003
Previous Showing 11-12 of 12 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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