A162356 a(n) = 8*a(n-1)-14*a(n-2) for n>1; a(0) = 2; a(1) = 9.

2, 9, 44, 226, 1192, 6372, 34288, 185096, 1000736, 5414544, 29306048, 158644768, 858873472, 4649961024, 25175459584, 136304222336, 737977344512, 3995559643392, 21632794323968, 117124519584256, 634137036138496

Offset

0,1

Comments

Fourth binomial transform of A135530.

Links

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

Index entries for linear recurrences with constant coefficients, signature (8,-14).

Formula

G.f.: (2-7*x)/(1-8*x+14*x^2).

a(n) = ((4+sqrt(2))^(n+1)+(4-sqrt(2))^(n+1))/4.

Prog

(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((4+r)^(n+1)+(4-r)^(n+1))/4: n in [0..20] ]; [ Integers()!S[j]: j in [1..#S] ];

Crossrefs

Cf. A135530, A161944 (third binomial transform of A135530), A161947 (fifth binomial transform of A135530).

Sequence in context: A216861 A199308 A176479 * A364476 A339440 A026302

Adjacent sequences: A162353 A162354 A162355 * A162357 A162358 A162359

Keyword

nonn,easy

Author

Klaus Brockhaus, Jul 01 2009

Status

approved