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A163309 a(n) = 18*a(n-1) - 76*a(n-2) for n > 1; a(0) = 1, a(1) = 10. 3
1, 10, 104, 1112, 12112, 133504, 1482560, 16539776, 185041408, 2073722368, 23263855616, 261146501120, 2932583993344, 32939377795072, 370032416817152, 4157190790283264, 46706970546995200, 524778969784385536 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A163308. Inverse binomial transform of A163310.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..950

Index entries for linear recurrences with constant coefficients, signature (18,-76).

FORMULA

a(n) = ((5+sqrt(5))*(9+sqrt(5))^n + (5-sqrt(5))*(9-sqrt(5))^n)/10.

G.f.: (1-8*x)/(1-18*x+76*x^2).

E.g.f.: (1/5)*exp(9*x)*(5*cosh(sqrt(5)*x) + sqrt(5)*sinh(sqrt(5)*x)). - G. C. Greubel, Dec 18 2016

MATHEMATICA

LinearRecurrence[{18, -76}, {1, 10}, 50] (* G. C. Greubel, Dec 18 2016 *)

PROG

(MAGMA) [ n le 2 select 9*n-8 else 18*Self(n-1)-76*Self(n-2): n in [1..18] ];

(PARI) Vec((1-8*x)/(1-18*x+76*x^2) + O(x^50)) \\ G. C. Greubel, Dec 18 2016

CROSSREFS

Cf. A163308, A163310.

Sequence in context: A227014 A036334 A190954 * A163165 A110957 A077671

Adjacent sequences:  A163306 A163307 A163308 * A163310 A163311 A163312

KEYWORD

nonn

AUTHOR

Klaus Brockhaus, Jul 24 2009

STATUS

approved

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Last modified April 19 21:57 EDT 2021. Contains 343117 sequences. (Running on oeis4.)