A162271 a(n) = ((5+sqrt(2))*(4+sqrt(2))^n + (5-sqrt(2))*(4-sqrt(2))^n)/2.

5, 22, 106, 540, 2836, 15128, 81320, 438768, 2371664, 12830560, 69441184, 375901632, 2035036480, 11017668992, 59650841216, 322959363840, 1748563133696, 9467073975808, 51256707934720, 277514627816448

Offset: 0

Author

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

Keywords

• nonn

Comments

Fourth binomial transform of A162396.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-14).

Crossrefs

Cf. A162396.

Programs

Magma

Z:=PolynomialRing(Integers()); N:=NumberField(x^2-2); S:=[ ((5+r)*(4+r)^n+(5-r)*(4-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 02 2009

Mathematica

LinearRecurrence[{8,-14}, {5,22}, 50] (* G. C. Greubel, Oct 02 2018 *)
Table[((5+Sqrt[2])(4+Sqrt[2])^n+(5-Sqrt[2])(4-Sqrt[2])^n)/2,{n,0,20}]// Simplify (* Harvey P. Dale, May 26 2019 *)

PARI

x='x+O('x^50); Vec((5-18*x)/(1-8*x+14*x^2)) \\ G. C. Greubel, Oct 02 2018

Formula

a(n) = 8*a(n-1) - 14*a(n-2) for n > 1; a(0) = 5, a(1) = 22.

G.f.: (5-18*x)/(1-8*x+14*x^2).

Extensions

Edited and extended beyond a(5) by Klaus Brockhaus, Jul 02 2009