(MAGMAMagma) [ n le 2 select 10*n-9 else 18*Self(n-1)-79*Self(n-2): n in [1..18] ];

reviewed

approved

proposed

reviewed

editing

proposed

a(n) = 18*a(n-1) - 79*a(n-2) for n > 1; a(0) = 1, a(1) = 11.

G. C. Greubel, <a href="/A163447/b163447.txt">Table of n, a(n) for n = 0..975</a>

<a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (18,-79).

a(n) = ((1+sqrt(2))*(9+sqrt(2))^n + (1-sqrt(2))*(9-sqrt(2))^n)/2.

E.g.f.: exp(9*x)*( cosh(sqrt(2)*x) + sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Dec 23 2016

LinearRecurrence[{18, -79}, {1, 11}, 50] (* G. C. Greubel, Dec 23 2016 *)

(PARI) Vec((1-7*x)/(1-18*x+79*x^2) + O(x^50)) \\ G. C. Greubel, Dec 23 2016

approved

editing

_Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), _, Jul 27 2009

a(n) = 18*a(n-1)-79*a(n-2) for n > 1; a(0) = 1, a(1) = 11.

1, 11, 119, 1273, 13513, 142667, 1500479, 15737929, 164744881, 1722111467, 17983160807, 187650088633, 1957031891641, 20402217047531, 212634387415919, 2215643826731593, 23083472275311073, 240466638643803467

0,2

Binomial transform of A163446. Inverse binomial transform of A163448.

a(n) = ((1+sqrt(2))*(9+sqrt(2))^n+(1-sqrt(2))*(9-sqrt(2))^n)/2.

G.f.: (1-7*x)/(1-18*x+79*x^2).

(MAGMA) [ n le 2 select 10*n-9 else 18*Self(n-1)-79*Self(n-2): n in [1..18] ];

Cf. A163446, A163448.

nonn

Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 27 2009

approved