A162815 - OEIS

A162815

a(n) = 8*a(n-1)-13*a(n-2) for n > 1; a(0) = 5, a(1) = 23.

5, 23, 119, 653, 3677, 20927, 119615, 684869, 3923957, 22488359, 128895431, 738814781, 4234877645, 24274429007, 139142022671, 797568604277, 4571702539493, 26205228460343, 150209694669335, 861009587370221

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OFFSET

0,1

COMMENTS

Binomial transform of A162814. Inverse binomial transform of A143647.

LINKS

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (8,-13)

FORMULA

a(n) = ((5+sqrt(3))*(4+sqrt(3))^n+(5-sqrt(3))*(4-sqrt(3))^n)/2.

G.f.: (5-17*x)/(1-8*x+13*x^2).

MATHEMATICA

LinearRecurrence[{8, -13}, {5, 23}, 20] (* Harvey P. Dale, Aug 25 2017 *)

PROG

(Magma) [ n le 2 select 18*n-13 else 8*Self(n-1)-13*Self(n-2): n in [1..20] ];

CROSSREFS

Cf. A162814, A143647.

Sequence in context: A005393 A193704 A294356 * A351756 A033312 A151881

Adjacent sequences: A162812 A162813 A162814 * A162816 A162817 A162818

KEYWORD

nonn,easy

AUTHOR

Klaus Brockhaus, Jul 18 2009

STATUS

approved