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A153598
a(n) = ((7 + sqrt(3))^n - (7 - sqrt(3))^n)/(2*sqrt(3)).
2
1, 14, 150, 1456, 13484, 121800, 1084936, 9586304, 84301200, 739246816, 6471600224, 56597049600, 494665084096, 4321846895744, 37751262672000, 329712720203776, 2879419999940864, 25145094869798400, 219578008179897856, 1917417750507843584
OFFSET
1,2
COMMENTS
lim_{n -> infinity} a(n)/a(n-1) = 7 + sqrt(3) = 8.73205080756887729....
FORMULA
G.f.: x/(1 - 14*x + 46*x^2). - Klaus Brockhaus, Dec 31 2008, (corrected Oct 11 2009)
a(n) = 14*a(n-1) - 46*a(n-2) for n>1; a(0)=0, a(1)=1. - Philippe Deléham, Jan 01 2009
MATHEMATICA
Join[{a=1, b=14}, Table[c=14*b-46*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *)
LinearRecurrence[{14, -46}, {1, 14}, 20] (* Harvey P. Dale, Dec 05 2015 *)
PROG
(Magma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-3); S:=[ ((7+r)^n-(7-r)^n)/(2*r): n in [1..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Dec 31 2008
(Magma) I:=[1, 14]; [n le 2 select I[n] else 14*Self(n-1)-46*Self(n-2): n in [1..25]]; // Vincenzo Librandi, Aug 23 2016
CROSSREFS
Cf. A002194 (decimal expansion of sqrt(3)).
Sequence in context: A019521 A009614 A009802 * A180347 A262183 A357484
KEYWORD
nonn
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Dec 29 2008
EXTENSIONS
Typo corrected and extended beyond a(7) by Klaus Brockhaus, Dec 31 2008
Edited by Klaus Brockhaus, Oct 11 2009
STATUS
approved