A164588 a(n) = ((3 + sqrt(18))*(5 + sqrt(8))^n + (3 - sqrt(18))*(5 - sqrt(8))^n)/6.

1, 9, 73, 577, 4529, 35481, 277817, 2174993, 17027041, 133295529, 1043495593, 8168931937, 63949894289, 500627099961, 3919122796697, 30680567267633, 240180585132481, 1880236207775049, 14719292130498313, 115228905772807297, 902061091509601649

Offset

0,2

Comments

Binomial transform of A057084. Second binomial transform of A002315. Third binomial transform of A108051 without initial 0. Fourth binomial transform of A096980. Fifth binomial transform of A094015.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (10,-17).

Formula

a(n) = 10*a(n-1) - 17*a(n-2) for n > 1; a(0) = 1, a(1) = 9.

G.f.: (1-x)/(1-10*x+17*x^2).

E.g.f.: (1/3)*exp(5*x)*(3*cosh(2*sqrt(2)*x) + 3*sqrt(2)*sinh(2*sqrt(2)*x)). - G. C. Greubel, Aug 12 2017

Mathematica

LinearRecurrence[{10, -17}, {1, 9}, 30] (* Harvey P. Dale, Sep 11 2016 *)

Prog

(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((3+3*r)*(5+2*r)^n+(3-3*r)*(5-2*r)^n)/6: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 24 2009
(PARI) x='x+O('x^50); Vec((1-x)/(1-10*x+17*x^2)) \\ G. C. Greubel, Aug 12 2017

Crossrefs

Cf. A057084, A002315, A108051, A096980, A094015.

Sequence in context: A126641 A346229 A081627 * A023001 A277672 A015454

Adjacent sequences: A164585 A164586 A164587 * A164589 A164590 A164591

Keyword

nonn

Author

Al Hakanson (hawkuu(AT)gmail.com), Aug 17 2009

Extensions

Extended by Klaus Brockhaus and R. J. Mathar Aug 24 2009

Status

approved