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A154240
a(n) = ( (8 + sqrt(6))^n - (8 - sqrt(6))^n )/(2*sqrt(6)).
1
1, 16, 198, 2240, 24356, 259776, 2743768, 28833280, 302193936, 3162772736, 33077115488, 345793029120, 3614215767616, 37771456592896, 394718790964608, 4124756173045760, 43102408892784896, 450402684247904256
OFFSET
1,2
COMMENTS
lim_{n -> infinity} a(n)/a(n-1) = 8 + sqrt(6) = 10.4494897427....
FORMULA
From Philippe Deléham, Jan 06 2009: (Start)
a(n) = 16*a(n-1) - 58*a(n-2) for n>1, with a(0)=0, a(1)=1.
G.f.: x/(1 - 16*x + 58*x^2). (End)
E.g.f.: sinh(sqrt(6)*x)*exp(8*x)/sqrt(6). - Ilya Gutkovskiy, Sep 07 2016
MATHEMATICA
Join[{a=1, b=16}, Table[c=16*b-58*a; a=b; b=c, {n, 40}]] (* Vladimir Joseph Stephan Orlovsky, Feb 08 2011*)
With[{s=Sqrt[6]}, Table[Simplify[((8+s)^n-(8-s)^n)/(2s)], {n, 20}]] (* or *) LinearRecurrence[{16, -58}, {1, 16}, 20] (* Harvey P. Dale, Jul 17 2013 *)
PROG
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-6); S:=[ ((8+r)^n-(8-r)^n)/(2*r): n in [1..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jan 07 2009
CROSSREFS
Cf. A010464 (decimal expansion of square root of 6).
Sequence in context: A153885 A016226 A332854 * A081679 A154249 A226869
KEYWORD
nonn
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Jan 05 2009
EXTENSIONS
Extended beyond a(7) by Klaus Brockhaus, Jan 07 2009
Edited by Klaus Brockhaus, Oct 06 2009
STATUS
approved