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.

A145301 a(n) = 12*a(n-1) - 30*a(n-2) with a(0)=1 and a(1)=6.

Original entry on oeis.org

1, 6, 42, 324, 2628, 21816, 182952, 1540944, 13002768, 109804896, 927575712, 7836761664, 66213868608, 559463573376, 4727146822272, 39941854665984, 337487851323648, 2851598575904256, 24094547371141632, 203586611176571904, 1720202912984613888
Offset: 0

Views

Author

Al Hakanson (hawkuu(AT)gmail.com), Oct 06 2008

Keywords

Comments

Binomial transform is A152262, inverse binomial transform is A146962.

Links

Crossrefs

Cf. A098158, A152262, A146962.

Programs

  • Magma
    Z:= PolynomialRing(Integers()); N:=NumberField(x^2-6); S:=[ ((6+r6)^n+(6-r6)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Oct 20 2008
  • Mathematica
    CoefficientList[Series[(1 - 6 x)/(1 - 12 x + 30 x^2), {x, 0, 20}], x] (* Wesley Ivan Hurt, Jun 14 2014 *)

Formula

G.f.: (1-6x)/(1-12x+30x^2). - R. J. Mathar, Oct 10 2008
a(n) = ((6+sqrt(6))^n+(6-sqrt(6))^n)/2.
a(n) = sum_{k, 0<=k<=n} 6^k * A098158(n,k). - Philippe Deléham, Oct 14 2008

Extensions

More terms from R. J. Mathar, Oct 10 2008
Corrected definition. - Philippe Deléham, Oct 15 2008
Edited by Klaus Brockhaus, Jul 08 2009

A152263 a(n) = ((8 + sqrt(6))^n + (8 - sqrt(6))^n)/2.

Original entry on oeis.org

1, 8, 70, 656, 6436, 64928, 665560, 6883136, 71527696, 745221248, 7774933600, 81176105216, 847871534656, 8857730451968, 92547138221440, 967005845328896, 10104359508418816, 105583413105625088, 1103281758201710080
Offset: 0

Views

Author

Al Hakanson (hawkuu(AT)gmail.com), Dec 01 2008

Keywords

Comments

Binomial transform of A152262. Inverse binomial transform of A152264. - Philippe Deléham, Dec 03 2008

Links

Programs

  • Magma
    Z:= PolynomialRing(Integers()); N:=NumberField(x^2-6); S:=[ ((8+r6)^n+(8-r6)^n)/2: n in [0..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Dec 03 2008
  • Mathematica
    LinearRecurrence[{16,-58},{1,8},20] (* Harvey P. Dale, Jul 09 2021 *)

Formula

From Philippe Deléham, Dec 03 2008: (Start)
a(n) = 16*a(n-1) - 58*a(n-2), n > 1; a(0)=1, a(1)=8.
G.f.: (1-8*x)/(1-16*x+58*x^2).
a(n) = Sum_{k=0..n} A098158(n,k)*8^(2k-n)*6^(n-k). (End)

Extensions

Extended beyond a(6) by Klaus Brockhaus, Dec 03 2008
Showing 1-2 of 2 results.

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