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A162773
a(n) = ((2+sqrt(5))*(5+sqrt(5))^n + (2-sqrt(5))*(5-sqrt(5))^n)/2.
4
2, 15, 110, 800, 5800, 42000, 304000, 2200000, 15920000, 115200000, 833600000, 6032000000, 43648000000, 315840000000, 2285440000000, 16537600000000, 119667200000000, 865920000000000, 6265856000000000, 45340160000000000
OFFSET
0,1
COMMENTS
Binomial transform of A162772. Fifth binomial transform of A162963.
FORMULA
a(n) = 10*a(n-1) - 20*a(n-2) for n > 1; a(0) = 2, a(1) = 15.
G.f.: (2-5*x)/(1-10*x+20*x^2).
MATHEMATICA
LinearRecurrence[{10, -20}, {2, 15}, 30] (* Harvey P. Dale, Dec 24 2012 *)
PROG
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-5); S:=[ ((2+r)*(5+r)^n+(2-r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 19 2009
CROSSREFS
Sequence in context: A037635 A154635 A062808 * A140637 A342963 A022026
KEYWORD
nonn
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Jul 13 2009
EXTENSIONS
Edited and extended beyond a(5) by Klaus Brockhaus, Jul 19 2009
Formulae corrected and clarified by Harvey P. Dale, Dec 24 2012
STATUS
approved