A143647 a(n) = ((5 + sqrt(3))^n + (5 - sqrt(3))^n)/2.
1, 5, 28, 170, 1084, 7100, 47152, 315320, 2115856, 14221520, 95666368, 643790240, 4333242304, 29169037760, 196359046912, 1321871638400, 8898817351936, 59906997474560, 403295993003008, 2715005985589760, 18277548009831424
Offset: 0
Keywords
Links
- Index entries for linear recurrences with constant coefficients, signature (10, -22).
Programs
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Magma
Z
:= PolynomialRing(Integers()); N :=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 -
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 *)
Formula
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
Extensions
More terms from Klaus Brockhaus and R. J. Mathar, Nov 01 2008
Edited by Klaus Brockhaus, Jul 15 2009
Comments