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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: A295118 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 December 16 06:18 EST 2019. Contains 330016 sequences. (Running on oeis4.)