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
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