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A143647
a(n) = ((5 + sqrt(3))^n + (5 - sqrt(3))^n)/2.
2
1, 5, 28, 170, 1084, 7100, 47152, 315320, 2115856, 14221520, 95666368, 643790240, 4333242304, 29169037760, 196359046912, 1321871638400, 8898817351936, 59906997474560, 403295993003008, 2715005985589760, 18277548009831424
OFFSET
0,2
COMMENTS
Binomial transform of A083882. - R. J. Mathar, Nov 01 2008
Inverse binomial transform of A147961.
FORMULA
From Philippe Deléham, Klaus Brockhaus and R. J. Mathar, Nov 01 2008: (Start)
a(n) = 10*a(n-1) - 22*a(n-2), a(0)=1, a(1)=5.
G.f.: (1-5x)/(1-10x+22*x^2). (End)
a(n) = (Sum_{k=0..n} A098158(n,k)*5^(2*k)*3^(n-k))/5^n. - Philippe Deléham, Nov 06 2008
MATHEMATICA
Simplify[With[{c=Sqrt[3]}, Table[((5+c)^n+(5-c)^n)/2, {n, 0, 25}]]] (* or *) LinearRecurrence[{10, -22}, {1, 5}, 25] (* Harvey P. Dale, Jun 04 2011 *)
PROG
(Magma) Z<x>:= PolynomialRing(Integers()); N<r3>:=NumberField(x^2-3); S:=[ ((5+r3)^n+(5-r3)^n)/2: n in [0..20] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Nov 01 2008
CROSSREFS
KEYWORD
nonn
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Oct 27 2008
EXTENSIONS
More terms from Klaus Brockhaus and R. J. Mathar, Nov 01 2008
Edited by Klaus Brockhaus, Jul 15 2009
STATUS
approved