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

0,2

Comments

Binomial transform of A083882. - R. J. Mathar, Nov 01 2008

Inverse binomial transform of A147961.

Links

Table of n, a(n) for n=0..20.

Index entries for linear recurrences with constant coefficients, signature (10, -22).

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

Cf. A083882, A147961, A098158.

Sequence in context: A272046 A370025 A292871 * A349318 A367889 A082031

Adjacent sequences: A143644 A143645 A143646 * A143648 A143649 A143650

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