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A163308 a(n) = 16*a(n-1) - 59*a(n-2) for n > 1; a(0) = 1, a(1) = 9. 3
1, 9, 85, 829, 8249, 83073, 842477, 8578325, 87547057, 894631737, 9148831429, 93598030381, 957787431785, 9802315116081, 100327583381981, 1026904742262917, 10511148456669793, 107590995513204585 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A163307. Inverse binomial transform of A163309.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..985

Index entries for linear recurrences with constant coefficients, signature (16, -59).

FORMULA

a(n) = ((5+sqrt(5))*(8+sqrt(5))^n + (5-sqrt(5))*(8-sqrt(5))^n)/10.

G.f.: (1-7*x)/(1-16*x+59*x^2).

E.g.f.: (1/5)*exp(8*x)*(5*cosh(sqrt(5)*x) + sqrt(5)*sinh(sqrt(5)*x)). - G. C. Greubel, Dec 18 2016

MATHEMATICA

LinearRecurrence[{16, -59}, {1, 9}, 20] (* Harvey P. Dale, Dec 06 2013 *)

PROG

(MAGMA) [ n le 2 select 8*n-7 else 16*Self(n-1)-59*Self(n-2): n in [1..18] ];

(PARI) Vec((1-7*x)/(1-16*x+59*x^2) + O(x^50)) \\ G. C. Greubel, Dec 18 2016

CROSSREFS

Cf. A163307, A163309.

Sequence in context: A339550 A228417 A015580 * A160112 A108427 A152106

Adjacent sequences:  A163305 A163306 A163307 * A163309 A163310 A163311

KEYWORD

nonn

AUTHOR

Klaus Brockhaus, Jul 24 2009

STATUS

approved

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Last modified May 7 23:48 EDT 2021. Contains 343652 sequences. (Running on oeis4.)