A163615 a(n) = ((1 + 3*sqrt(2))*(4 + sqrt(2))^n + (1 - 3*sqrt(2))*(4 - sqrt(2))^n)/2.

1, 10, 66, 388, 2180, 12008, 65544, 356240, 1932304, 10471072, 56716320, 307135552, 1663055936, 9004549760, 48753614976, 263965223168, 1429171175680, 7737856281088, 41894453789184, 226825642378240, 1228082785977344

Offset

0,2

Comments

Binomial transform of A163614. Fourth binomial transform of A163864. Inverse binomial transform of A163616.

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) = 10.

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

E.g.f.: exp(4*x)*( cosh(sqrt(2)*x) + 3*sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Jul 30 2017

Mathematica

LinearRecurrence[{8, -14}, {1, 10}, 30] (* Harvey P. Dale, Jun 11 2014 *)

Prog

(Magma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+3*r)*(4+r)^n+(1-3*r)*(4-r)^n)/2: n in [0..20] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 06 2009
(PARI) x='x+O('x^50); Vec((1+2*x)/(1-8*x+14*x^2)) \\ G. C. Greubel, Jul 30 2017

Crossrefs

Cf. A163614, A163864, A163616.

Sequence in context: A026853 A177452 A033504 * A232062 A229003 A117305

Adjacent sequences: A163612 A163613 A163614 * A163616 A163617 A163618

Keyword

nonn

Author

Al Hakanson (hawkuu(AT)gmail.com), Aug 01 2009

Extensions

Edited and extended beyond a(5) by Klaus Brockhaus, Aug 06 2009

Status

approved