A163446 a(n) = 16*a(n-1) - 62*a(n-2) for n > 1; a(0) = 1, a(1) = 10.

1, 10, 98, 948, 9092, 86696, 823432, 7799760, 73743376, 696308896, 6568853024, 61930496832, 583619061824, 5498214185600, 51787045136512, 487703442676992, 4592458284368128, 43241719103916544, 407135092031840768

Offset: 0

Author

Klaus Brockhaus, Jul 27 2009

Keywords

• nonn

Comments

Binomial transform of A163445. Inverse binomial transform of A163447.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (16,-62).

Crossrefs

Cf. A163445, A163447.

Programs

Magma

[ n le 2 select 9*n-8 else 16*Self(n-1)-62*Self(n-2): n in [1..19] ];

Mathematica

LinearRecurrence[{16,-62},{1,10},30] (* Harvey P. Dale, Sep 25 2015 *)

PARI

Vec((1-6*x)/(1-16*x+62*x^2) + O(x^50)) \\ G. C. Greubel, Dec 23 2016

Formula

a(n) = ((1+sqrt(2))*(8+sqrt(2))^n + (1-sqrt(2))*(8-sqrt(2))^n)/2.

G.f.: (1-6*x)/(1-16*x+62*x^2).

E.g.f.: exp(8*x)*( cosh(sqrt(2)*x) + sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Dec 23 2016