OFFSET
1,2
COMMENTS
Fourth binomial transform of A055845.
lim_{n -> infinity} a(n)/a(n-1) = 6 + sqrt(3) = 7.73205080756887729....
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (12,-33).
FORMULA
G.f.: x/(1 - 12*x + 33*x^2). - Klaus Brockhaus, Dec 31 2008, (corrected Oct 11 2009)
a(n) = 12*a(n-1) - 33*a(n-2) for n>1; a(0)=0, a(1)=1. - Philippe Deléham, Jan 01 2009
E.g.f.: sinh(sqrt(3)*x)*exp(6*x)/sqrt(3). - Ilya Gutkovskiy, Aug 23 2016
MATHEMATICA
LinearRecurrence[{12, -33}, {1, 12}, 25] (* G. C. Greubel, Aug 22 2016 *)
PROG
(Magma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-3); S:=[ ((6+r)^n-(6-r)^n)/(2*r): n in [1..20] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Dec 31 2008
(Sage) [lucas_number1(n, 12, 33) for n in range(1, 21)] # Zerinvary Lajos, Apr 27 2009
(Magma) I:=[1, 12]; [n le 2 select I[n] else 12*Self(n-1)-33*Self(n-2): n in [1..25]]; // Vincenzo Librandi, Aug 23 2016
KEYWORD
nonn
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Dec 29 2008
EXTENSIONS
Extended beyond a(7) by Klaus Brockhaus, Dec 31 2008
Edited by Klaus Brockhaus, Oct 11 2009
STATUS
approved