A163350 a(n) = 8*a(n-1) - 14*a(n-2) for n > 1; a(0) = 1, a(1) = 6.

1, 6, 34, 188, 1028, 5592, 30344, 164464, 890896, 4824672, 26124832, 141453248, 765878336, 4146681216, 22451153024, 121555687168, 658129355008, 3563255219712, 19292230787584, 104452273224704, 565526954771456

Offset

0,2

Comments

Binomial transform of A102285. Fourth binomial transform of A163403. Inverse binomial transform of A163346.

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = 8*a(n-1) - 14*a(n-2) for n > 1; a(0) = 1, a(1) = 6.

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

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

E.g.f.: exp(4*x)*( cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Dec 19 2016

Mathematica

LinearRecurrence[{8, -14}, {1, 6}, 30] (* Harvey P. Dale, May 08 2014 *)

Prog

(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+r)*(4+r)^n+(1-r)*(4-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 26 2009
(PARI) Vec((1-2*x)/(1-8*x+14*x^2) + O(x^50)) \\ G. C. Greubel, Dec 19 2016

Crossrefs

Cf. A102285, A163403, A163346.

Sequence in context: A229009 A085351 A125343 * A320746 A320749 A052264

Adjacent sequences: A163347 A163348 A163349 * A163351 A163352 A163353

Keyword

nonn,easy

Author

Al Hakanson (hawkuu(AT)gmail.com), Jul 25 2009

Extensions

Edited and extended beyond a(5) by Klaus Brockhaus, Jul 26 2009

New name from G. C. Greubel, Dec 19 2016

Status

approved