A164311 a(n) = 12*a(n-1) - 33*a(n-2) for n > 1; a(0) = 4, a(1) = 27.

4, 27, 192, 1413, 10620, 80811, 619272, 4764501, 36738036, 283627899, 2191179600, 16934434533, 130904287596, 1012015111563, 7824339848088, 60495579495477, 467743738958820, 3616570744155099, 27963305544220128, 216212831973523269

Offset: 0

Author

Klaus Brockhaus, Aug 12 2009

Keywords

• nonn
• easy

Comments

Binomial transform of A162561. Sixth binomial transform of A162766.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (12,-33).

Crossrefs

Cf. A162561, A162766.

Programs

Magma

[ n le 2 select 23*n-19 else 12*Self(n-1)-33*Self(n-2): n in [1..20] ];

Mathematica

LinearRecurrence[{12,-33}, {4,27}, 50] (* or *) CoefficientList[Series[(4 - 21*x)/(1 - 12*x + 33*x^2), {x,0,50}], x] (* G. C. Greubel, Sep 13 2017 *)

PARI

x='x+O('x^50); Vec((4-21*x)/(1-12*x+33*x^2)) \\ G. C. Greubel, Sep 13 2017

Formula

a(n) = ((4+sqrt(3))*(6+sqrt(3))^n + (4-sqrt(3))*(6-sqrt(3))^n)/2.

G.f.: (4-21*x)/(1-12*x+33*x^2).

E.g.f.: (4*cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x))*exp(6*x). - G. C. Greubel, Sep 13 2017