A164310 a(n) = 6*a(n-1) - 6*a(n-2) for n > 1; a(0) = 4, a(1) = 15.

4, 15, 66, 306, 1440, 6804, 32184, 152280, 720576, 3409776, 16135200, 76352544, 361304064, 1709709120, 8090430336, 38284327296, 181163381760, 857274326784, 4056665670144, 19196348060160, 90838094340096, 429850477679616

Offset: 0

Author

Klaus Brockhaus, Aug 12 2009

Keywords

• nonn
• easy

Comments

Binomial transform of A077236. Inverse binomial transform of A083882 without initial 1.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-6).

Crossrefs

Cf. A077236, A083882.

Programs

Magma

[ n le 2 select 11*n-7 else 6*Self(n-1)-6*Self(n-2): n in [1..22] ];

Mathematica

LinearRecurrence[{6,-6}, {4,15}, 50] (* or *) CoefficientList[Series[(4 - 9*x)/(1 - 6*x + 6*x^2), {x,0,50}], x] (* G. C. Greubel, Sep 13 2017 *)

PARI

x='x+O('x^50); Vec((4-9*x)/(1-6*x+6*x^2)) \\ G. C. Greubel, Sep 13 2017

Formula

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

G.f.: (4-9*x)/(1-6*x+6*x^2).

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