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A163306 a(n) = 12*a(n-1) - 31*a(n-2) for n > 1; a(0) = 1, a(1) = 7. 2
1, 7, 53, 419, 3385, 27631, 226637, 1863083, 15331249, 126219415, 1039364261, 8559569267, 70494539113, 580587822079, 4781723152445, 39382455344891, 324356046412897, 2671416441263143, 22001959856357909, 181209608597137475 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A090041. Inverse binomial transform of A163307.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (12,-31).

FORMULA

a(n) = ((5+sqrt(5))*(6+sqrt(5))^n + (5-sqrt(5))*(6-sqrt(5))^n)/10.

G.f.: (1-5*x)/(1-12*x+31*x^2).

E.g.f.: (1/5)*exp(6*x)*(5*cosh(sqrt(5)*x) + sqrt(5)*sinh(sqrt(5)*x)). - G. C. Greubel, Dec 18 2016

MATHEMATICA

LinearRecurrence[{12, -31}, {1, 7}, 50] (* G. C. Greubel, Dec 18 2016 *)

PROG

(MAGMA) [ n le 2 select 6*n-5 else 12*Self(n-1)-31*Self(n-2): n in [1..20] ];

(PARI) Vec((1-5*x)/(1-12*x+31*x^2) + O(x^50)) \\ G. C. Greubel, Dec 18 2016

CROSSREFS

Cf. A090041, A163307.

Sequence in context: A279269 A015561 A133588 * A081338 A142981 A120272

Adjacent sequences:  A163303 A163304 A163305 * A163307 A163308 A163309

KEYWORD

nonn,easy

AUTHOR

Klaus Brockhaus, Jul 24 2009

STATUS

approved

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Last modified February 16 15:17 EST 2020. Contains 331961 sequences. (Running on oeis4.)