A162274 a(n) = ((2+sqrt(3))*(4+sqrt(3))^n + (2-sqrt(3))*(4-sqrt(3))^n)/2.

2, 11, 62, 353, 2018, 11555, 66206, 379433, 2174786, 12465659, 71453054, 409570865, 2347677218, 13456996499, 77136168158, 442148390777, 2534416940162, 14527406441195, 83271831307454, 477318366724097

Offset

0,1

Comments

Binomial transform of A162273, inverse binomial transform of A162275.

Links

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (8, -13).

Formula

a(n) = 8*a(n-1) - 13*a(n-2) for n > 1; a(0) = 2, a(1) = 11.

G.f.: (2-5*x)/(1-8*x+13*x^2).

Maple

a := proc (n) options operator, arrow; expand((1/2)*(2+sqrt(3))*(4+sqrt(3))^n+(1/2)*(2-sqrt(3))*(4-sqrt(3))^n) end proc: seq(a(n), n = 0 .. 20); # Emeric Deutsch, Jul 09 2009

Prog

(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-3); S:=[ ((2+r)*(4+r)^n+(2-r)*(4-r)^n)/2: n in [0..21] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 05 2009

Crossrefs

Cf. A162273, A162275.

Sequence in context: A308729 A034726 A256933 * A183160 A020078 A365131

Adjacent sequences: A162271 A162272 A162273 * A162275 A162276 A162277

Keyword

nonn

Author

Al Hakanson (hawkuu(AT)gmail.com), Jun 29 2009

Extensions

Edited and extended beyond a(5) by Klaus Brockhaus, Jul 05 2009

Status

approved