A143647 -id:A143647 - cp's OEIS frontend

A162815 a(n) = 8a(n-1)-13a(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

Offset: 0

Klaus Brockhaus, Jul 18 2009

Binomial transform of A162814. Inverse binomial transform of A143647.

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

Cf. A162814, A143647.

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

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

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).

A162816 a(n) = 12a(n-1)-33a(n-2) for n > 1; a(0) = 5, a(1) = 33.

Original entry on oeis.org

5, 33, 231, 1683, 12573, 95337, 729135, 5603499, 43180533, 333250929, 2574053559, 19891362051, 153752577165, 1188615978297, 9189556693119, 71050353033627, 549348865530597, 4247524736257473, 32841784272579975, 253933094974463091

Offset: 0

Klaus Brockhaus, Jul 14 2009

Binomial transform of A143647.

Index entries for linear recurrences with constant coefficients, signature (12,-33).

Cf. A143647.

[ n le 2 select 28*n-23 else 12*Self(n-1)-33*Self(n-2): n in [1..20] ];

LinearRecurrence[{12,-33},{5,33},40] (* or *) Simplify[With[ {c=Sqrt[3]},Table[(11(5+c)(6+c)^n+(53+7c)(6-c)^n)/(22(6+c)),{n,30}]]] (* Harvey P. Dale, Jun 30 2011 *)

Vec((5-27*x)/(1-12*x+33*x^2)+O(x^99)) \\ Charles R Greathouse IV, Jun 30 2011

a(n) = ((5+sqrt(3))*(6+sqrt(3))^n+(5-sqrt(3))*(6-sqrt(3))^n)/2.

G.f.: (5-27*x)/(1-12*x+33*x^2).

cp's OEIS Frontend

A162815 a(n) = 8a(n-1)-13a(n-2) for n > 1; a(0) = 5, a(1) = 23.

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A162816 a(n) = 12a(n-1)-33a(n-2) for n > 1; a(0) = 5, a(1) = 33.

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cp's OEIS Frontend

A162815 a(n) = 8*a(n-1)-13*a(n-2) for n > 1; a(0) = 5, a(1) = 23.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

Formula

A162816 a(n) = 12*a(n-1)-33*a(n-2) for n > 1; a(0) = 5, a(1) = 33.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

A162815 a(n) = 8a(n-1)-13a(n-2) for n > 1; a(0) = 5, a(1) = 23.

A162816 a(n) = 12a(n-1)-33a(n-2) for n > 1; a(0) = 5, a(1) = 33.