A163604 a(n) = ((3+2*sqrt(2))*(4+sqrt(2))^n + (3-2*sqrt(2))*(4-sqrt(2))^n)/2.

3, 16, 86, 464, 2508, 13568, 73432, 397504, 2151984, 11650816, 63078752, 341518592, 1849046208, 10011109376, 54202228096, 293462293504, 1588867154688, 8602465128448, 46575580861952, 252170135097344, 1365302948711424, 7392041698328576, 40022092304668672

Offset

0,1

Comments

Binomial transform of A163606. Inverse binomial transform of A163605.

Links

G. C. Greubel, 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) = 3, a(1) = 16.

G.f.: (3-8*x)/(1-8*x+14*x^2).

E.g.f.: exp(4*x)*( 3*cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Jul 29 2017

Mathematica

LinearRecurrence[{8, -14}, {3, 16}, 50] (* G. C. Greubel, Jul 29 2017 *)

Prog

(Magma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((3+2*r)*(4+r)^n+(3-2*r)*(4-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 07 2009
(PARI) x='x+O('x^50); Vec((3-8*x)/(1-8*x+14*x^2)) \\ G. C. Greubel, Jul 29 2017

Crossrefs

Cf. A163606, A163605.

Sequence in context: A056360 A278681 A224869 * A151329 A356402 A347930

Adjacent sequences: A163601 A163602 A163603 * A163605 A163606 A163607

Keyword

nonn

Author

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

Extensions

Edited and extended beyond a(5) by Klaus Brockhaus and R. J. Mathar, Aug 07 2009

Status

approved