A162275 a(n) = 10*a(n-1) - 22*a(n-2) for n > 1; a(0) = 2, a(1) = 13.

2, 13, 86, 574, 3848, 25852, 173864, 1169896, 7873952, 53001808, 356791136, 2401871584, 16169310848, 108851933632, 732794497664, 4933202436736, 33210545418752, 223575000579328, 1505118006580736, 10132530053062144, 68212704385845248, 459211382691085312

Offset: 0

Author

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

Keywords

• nonn
• easy

Comments

Binomial transform of A162274.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..149
• Index entries for linear recurrences with constant coefficients, signature (10, -22).

Crossrefs

Cf. A162274.

Programs

Magma

Z:=PolynomialRing(Integers()); N:=NumberField(x^2-3); 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 05 2009

Maple

a := proc (n) options operator, arrow; expand((1/2)*(2+sqrt(3))*(5+sqrt(3))^n+(1/2)*(2-sqrt(3))*(5-sqrt(3))^n) end proc: seq(a(n), n = 0 .. 20); # Emeric Deutsch, Jul 09 2009

Mathematica

CoefficientList[Series[(2 - 7 z)/(22 z^2 - 10 z + 1), {z, 0, 200}], z] (* Vladimir Joseph Stephan Orlovsky, Jun 12 2011 *)
LinearRecurrence[{10,-22},{2,13},30] (* Harvey P. Dale, Jun 14 2017 *)

Formula

a(n) = 10*a(n-1) - 22*a(n-2) for n > 1; a(0) = 2, a(1) = 13.

a(n) = ((2+sqrt(3))*(5+sqrt(3))^n + (2-sqrt(3))*(5-sqrt(3))^n)/2.

G.f.: (2-7*x)/(1-10*x+22*x^2).

Extensions

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