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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A317199 Bo Tan et al.'s string E_n, defined by A_n = A103269(n) = D_{n-1}E_n = A317197(n-1)E_n for n >= 2, with E_1 = 12.

Original entry on oeis.org

12, 213, 3121, 121312, 2131211213
Offset: 1

Views

Author

N. J. A. Sloane, Aug 05 2018

Keywords

Comments

See A317200 for length of E_n.

Examples

			A_4 = 1213121121312, D_3 = 1213121, so E_4 = 121312.

Links

Crossrefs

Cf. A103269, A317197, A317200.
See A317201 for the reversals of these words.

A027084 G.f.: x^2*(x^2 + x + 1)/(x^4 - 2*x + 1).

Original entry on oeis.org

1, 3, 7, 14, 27, 51, 95, 176, 325, 599, 1103, 2030, 3735, 6871, 12639, 23248, 42761, 78651, 144663, 266078, 489395, 900139, 1655615, 3045152, 5600909, 10301679, 18947743, 34850334, 64099759, 117897839, 216847935, 398845536
Offset: 2

Views

Author

Clark Kimberling

Keywords

Comments

Lengths of palindromic prefixes of the ternary tribonacci word A080843 [A. Glen]. - N. J. A. Sloane, Jun 09 2019
Original definition was: a(n) = (1/2)*T(n,n+2), T given by A027082.

Links

Crossrefs

Cf. A000073, A008937, A018921, A027082, A080843, A317197 (D_n).

Programs

  • PARI
    Vec(x^2*(x^2 + x + 1)/(x^4 - 2*x + 1) + O(x^50)) \\ Michel Marcus, Dec 29 2014

Formula

Positive numbers of the form (t_n + t_{n+2} - 3)/2, n>1, where {t_n} are the tribonacci numbers A000073 [A. Glen]. See Mousavi-Shallit, 2014. - N. J. A. Sloane, Jun 09 2019
a(n) = A008937(n-1) - 1 = A018921(n-3) - 1.
2*a(n) = A000213(n+2)-3. - R. J. Mathar, Jun 24 2020

Extensions

Entry revised by N. J. A. Sloane, Aug 05 2018
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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