A053469 a(n) = n*6^(n-1).

1, 12, 108, 864, 6480, 46656, 326592, 2239488, 15116544, 100776960, 665127936, 4353564672, 28298170368, 182849716224, 1175462461440, 7522959753216, 47958868426752, 304679870005248, 1929639176699904, 12187194800209920, 76779327241322496, 482612914088312832

Offset

1,2

Comments

Binomial transform of A053464. - R. J. Mathar, Oct 26 2011

References

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..400

Frank Ellermann, Illustration of binomial transforms.

Index entries for linear recurrences with constant coefficients, signature (12,-36).

Formula

a(n) = 12*a(n-1) - 36*a(n-2), n>=3.

G.f.: x/(6x-1)^2. - Zerinvary Lajos, Apr 28 2009

E.g.f.: x*exp(6*x). - Michael Somos, Dec 16 2019

From Amiram Eldar, Oct 28 2020: (Start)

Sum_{n>=1} 1/a(n) = 6*log(6/5).

Sum_{n>=1} (-1)^(n+1)/a(n) = 6*log(7/6). (End)

Example

G.f. = x + 12*x^2 + 108*x^3 + 864*x^4 + 6480*x^5 + 46656*x^6 + ... - Michael Somos, Dec 16 2019

Mathematica

f[n_]:=n*6^(n-1); f[Range[40]] (* Vladimir Joseph Stephan Orlovsky, Feb 09 2011 *)
LinearRecurrence[{12, -36}, {1, 12}, 20] (* Harvey P. Dale, Apr 28 2015 *)

Prog

(Sage) [lucas_number1(n, 12, 36) for n in range(1, 21)] # Zerinvary Lajos, Apr 28 2009
(Magma) [n*(6^(n-1)): n in [1..30]]; // Vincenzo Librandi, Jun 09 2011
(PARI) a(n)=n*6^(n-1) \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A002697, A027471.

Sequence in context: A353047 A037972 A111990 * A055533 A037602 A037707

Adjacent sequences: A053466 A053467 A053468 * A053470 A053471 A053472

Keyword

easy,nonn

Author

Barry E. Williams, Jan 13 2000

Extensions

More terms from James A. Sellers, Feb 02 2000

More terms from Zerinvary Lajos, Oct 02 2007

Status

approved