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.

A164682 a(n) = 2*a(n-2) for n > 2; a(1) = 5, a(2) = 8.

Original entry on oeis.org

5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 512, 640, 1024, 1280, 2048, 2560, 4096, 5120, 8192, 10240, 16384, 20480, 32768, 40960, 65536, 81920, 131072, 163840, 262144, 327680, 524288, 655360, 1048576, 1310720, 2097152, 2621440, 4194304
Offset: 1

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Author

Klaus Brockhaus, Aug 21 2009

Keywords

Comments

Interleaving of A020714 and A000079 without initial terms 1, 2, 4.
First differences are in A162255.
Binomial transform is A135532 without initial terms -1, 3. Fourth binomial transform is A164537.

Links

Crossrefs

Equals A094958 (numbers of the form 2^n or 5*2^n) without initial terms 1, 2, 4.
Cf. A020714 (5*2^n), A000079 (powers of 2), A162255, A135532, A164537.

Programs

  • Magma
    [ n le 2 select 2+3*n else 2*Self(n-2): n in [1..40] ];
  • Mathematica
    LinearRecurrence[{0,2},{5,8},60] (* Harvey P. Dale, Jul 20 2022 *)

Formula

a(n) = (9-(-1)^n)*2^(1/4*(2*n-5+(-1)^n)).
G.f.: x*(5+8*x)/(1-2*x^2).

A164538 a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 5, a(1) = 33.

Original entry on oeis.org

5, 33, 215, 1391, 8965, 57657, 370375, 2377639, 15257765, 97891953, 627990935, 4028394431, 25840152805, 165748456137, 1063161046855, 6819395977399, 43741255696325, 280566449483073, 1799615613815255, 11543127800041871
Offset: 0

Views

Author

Al Hakanson (hawkuu(AT)gmail.com), Aug 15 2009

Keywords

Comments

Binomial transform of A164537. Fifth binomial transform of A164682.

Links

Crossrefs

Cf. A164537, A164682.

Programs

  • Magma
    Z:=PolynomialRing(Integers()); N:=NumberField(x^2-2); S:=[ ((5+4*r)*(5+r)^n+(5-4*r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 21 2009
  • Mathematica
    LinearRecurrence[{10,-23},{5,33},20] (* Harvey P. Dale, May 29 2019 *)
  • PARI
    Vec((5-17*x)/(1-10*x+23*x^2)+O(x^99)) \\ Charles R Greathouse IV, Jun 14 2011

Formula

a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 5, a(1) = 33.
G.f.: (5-17*x)/(1-10*x+23*x^2).
a(n) = ((5+4*sqrt(2))*(5+sqrt(2))^n + (5-4*sqrt(2))*(5-sqrt(2))^n)/2.

Extensions

Edited and extended beyond a(5) by Klaus Brockhaus, Aug 21 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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