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A162272
a(n) = ((1+sqrt(3))*(5+sqrt(3))^n + (1-sqrt(3))*(5-sqrt(3))^n)/2.
4
1, 8, 58, 404, 2764, 18752, 126712, 854576, 5758096, 38780288, 261124768, 1758081344, 11836068544, 79682895872, 536435450752, 3611330798336, 24311728066816, 163668003104768, 1101822013577728, 7417524067472384, 49935156376013824, 336166034275745792, 2263086902485153792
OFFSET
0,2
COMMENTS
Fifth binomial transform of A162436, binomial transform of A161728.
FORMULA
From Emeric Deutsch, Jul 05 2009: (Start)
G.f.: (1 - 2*x)/(1 - 10*x + 22*x^2).
a(n) = 10*a(n-1) - 22*a(n-2) for n >= 2; a(0)=1, a(1)=8. (End)
E.g.f.: exp(5*x)*(cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x)). - Stefano Spezia, Dec 31 2022
MAPLE
seq(expand(((1+sqrt(3))*(5+sqrt(3))^n+(1-sqrt(3))*(5-sqrt(3))^n)*1/2), n = 0 .. 20); # Emeric Deutsch, Jul 05 2009
MATHEMATICA
LinearRecurrence[{10, -22}, {1, 8}, 40] (* Vincenzo Librandi, Feb 03 2018 *)
PROG
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-3); S:=[ ((1+r)*(5+r)^n+(1-r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 02 2009
CROSSREFS
Sequence in context: A297097 A081897 A125371 * A273584 A037532 A062236
KEYWORD
nonn,easy
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Jun 29 2009
EXTENSIONS
Edited and extended beyond a(5) by Klaus Brockhaus, Jul 05 2009
Extended by Emeric Deutsch, Jul 05 2009
STATUS
approved