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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A162766 a(n) = 3*a(n-2) for n > 2; a(1) = 4, a(2) = 3.

Original entry on oeis.org

4, 3, 12, 9, 36, 27, 108, 81, 324, 243, 972, 729, 2916, 2187, 8748, 6561, 26244, 19683, 78732, 59049, 236196, 177147, 708588, 531441, 2125764, 1594323, 6377292, 4782969, 19131876, 14348907, 57395628, 43046721, 172186884, 129140163
Offset: 1

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Author

Klaus Brockhaus, Jul 13 2009

Keywords

Comments

Binomial transform is A162559. Second binomial transform is A077236.

Links

Crossrefs

Cf. A074324, A166552, A162559, A077236, A162436.

Programs

  • Magma
    [ n le 2 select 5-n else 3*Self(n-2): n in [1..34] ];
  • PARI
    a(n)=3^(n\2)*4^(n%2) \\ M. F. Hasler, Dec 03 2014

Formula

a(n) = (5-3*(-1)^n)*3^(1/4*(2*n-1+(-1)^n))/2.
G.f.: x*(4+3*x)/(1-3*x^2).
a(n) = A074324(n+1) = A166552(n+1) = 3^floor(n/2)*4^(n%2), where n%2 = 0 for n even, 1 for n odd. - M. F. Hasler, Dec 03 2014

Extensions

G.f. corrected by Klaus Brockhaus, Sep 18 2009

A162561 a(n) = ((4+sqrt(3))*(5+sqrt(3))^nv+v(4-sqrt(3))*(5-sqrt(3))^n)/2.

Original entry on oeis.org

4, 23, 142, 914, 6016, 40052, 268168, 1800536, 12105664, 81444848, 548123872, 3689452064, 24835795456, 167190009152, 1125512591488, 7576945713536, 51008180122624, 343388995528448, 2311709992586752, 15562542024241664
Offset: 0

Views

Author

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

Keywords

Comments

Third binomial transform of A077236. Fourth binomial transform of A162559. Fifth binomial transform of A162766.

Links

Crossrefs

Cf. A077236, A162559, A162766.

Programs

  • Magma
    Z:=PolynomialRing(Integers()); N:=NumberField(x^2-3); S:=[ ((4+r)*(5+r)^n+(4-r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 14 2009
  • Mathematica
    LinearRecurrence[{10,-22},{4,23},30] (* Harvey P. Dale, Mar 27 2013 *)

Formula

a(n) = 10*a(n-1) - 22*a(n-2) for n > 2; a(0) = 4, a(1) = 23.
G.f.: (4-17*x)/(1-10*x+22*x^2).

Extensions

Edited and extended beyond a(5) by Klaus Brockhaus, Jul 14 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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