A163461 a(n) = 18*a(n-1) - 79*a(n-2) for n > 1; a(0) = 1, a(1) = 10.

1, 10, 101, 1028, 10525, 108238, 1116809, 11551760, 119703769, 1242078802, 12900820685, 134090546972, 1394465011381, 14507216994070, 150967169994161, 1571338917363368, 16357694083001905, 170302719022328218

Offset

0,2

Comments

Binomial transform of A163460. Inverse binomial transform of A163462.

Links

G. C. Greubel, Table of n, a(n) for n = 0..975

Index entries for linear recurrences with constant coefficients, signature (18, -79).

Formula

a(n) = ((2+sqrt(2))*(9+sqrt(2))^n + (2-sqrt(2))*(9-sqrt(2))^n)/4.

G.f.: (1-8*x)/(1-18*x+79*x^2).

E.g.f.: (1/2)*exp(9*x)*(2*cosh(sqrt(2)*x) + sqrt(2)*sinh(sqrt(2)*x)). - G. C. Greubel, Dec 24 2016

Mathematica

LinearRecurrence[{18, -79}, {1, 10}, 30] (* Harvey P. Dale, Jul 25 2013 *)

Prog

(Magma) [ n le 2 select 9*n-8 else 18*Self(n-1)-79*Self(n-2): n in [1..18] ];
(PARI) Vec((1-8*x)/(1-18*x+79*x^2) + O(x^50)) \\ G. C. Greubel, Dec 24 2016

Crossrefs

Cf. A163460, A163462.

Sequence in context: A261199 A041041 A333344 * A081192 A288809 A288895

Adjacent sequences: A163458 A163459 A163460 * A163462 A163463 A163464

Keyword

nonn

Author

Klaus Brockhaus, Jul 28 2009

Status

approved