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.

A162813 a(n) = 3*a(n-2) for n > 2; a(1) = 5, a(2) = 3.

Original entry on oeis.org

5, 3, 15, 9, 45, 27, 135, 81, 405, 243, 1215, 729, 3645, 2187, 10935, 6561, 32805, 19683, 98415, 59049, 295245, 177147, 885735, 531441, 2657205, 1594323, 7971615, 4782969, 23914845, 14348907, 71744535, 43046721, 215233605, 129140163, 645700815, 387420489
Offset: 1

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Author

Klaus Brockhaus, Jul 20 2009

Keywords

Comments

Binomial transform is A162562.

Links

Crossrefs

Cf. A162562, A162436, A162766.

Programs

  • Magma
    [ n le 2 select 7-2*n else 3*Self(n-2): n in [1..34] ];
  • Mathematica
    nxt[{a_,b_}]:={b,3a}; NestList[nxt,{5,3},40][[All,1]] (* or *) LinearRecurrence[ {0,3},{5,3},40] (* Harvey P. Dale, May 29 2021 *)

Formula

a(n) = (3-2*(-1)^n)*3^(1/4*(2*n-1+(-1)^n)).
G.f.: x*(5+3*x)/(1-3*x^2)

Extensions

a(35)-a(36) from Yifan Xie, Jul 20 2022

A162563 a(n) = ((5+sqrt(3))*(2+sqrt(3))^n + (5-sqrt(3))*(2-sqrt(3))^n)/2.

Original entry on oeis.org

5, 13, 47, 175, 653, 2437, 9095, 33943, 126677, 472765, 1764383, 6584767, 24574685, 91713973, 342281207, 1277410855, 4767362213, 17792037997, 66400789775, 247811121103, 924843694637, 3451563657445, 12881410935143, 48074080083127
Offset: 0

Views

Author

Al Hakanson (hawkuu(AT)gmail.com), Jul 06 2009

Keywords

Comments

Binomial transform of A162562. Second binomial transform of A162813. Inverse binomial transform of A162814.

Links

Crossrefs

Cf. A162562, A162813, A162814.

Programs

  • Magma
    Z:=PolynomialRing(Integers()); N:=NumberField(x^2-3); S:=[ ((5+r)*(2+r)^n+(5-r)*(2-r)^n)/2: n in [0..25] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 14 2009
  • Mathematica
    LinearRecurrence[{4,-1},{5,13},30] (* Harvey P. Dale, Aug 25 2014 *)

Formula

a(n) = 4*a(n-1) - a(n-2) for n > 1; a(0) = 5, a(1) = 13.
G.f.: (5-7*x)/(1-4*x+x^2).
a(n) = 4*a(n-1) - a(n-2), with a(0)=5 and a(1)=13. - Paolo P. Lava, Jul 15 2009

Extensions

Edited and extended beyond a(5) by Klaus Brockhaus, Jul 18 2009
Showing 1-2 of 2 results.

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

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