A164072 a(n) = 8*a(n-1) - 14*a(n-2) for n > 1; a(0) = 1, a(1) = 7.

1, 7, 42, 238, 1316, 7196, 39144, 212408, 1151248, 6236272, 33772704, 182873824, 990172736, 5361148352, 29026768512, 157158071168, 850889810176, 4606905485056, 24942786537984, 135045615513088, 731165912572928

Offset: 0

Author

Klaus Brockhaus, Aug 09 2009

Keywords

• nonn

Comments

Binomial transform of A081179 without initial 0. Inverse binomial transform of A164031.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-14).

Crossrefs

Cf. A081179, A164031.

Programs

Magma

[ n le 2 select 6*n-5 else 8*Self(n-1)-14*Self(n-2): n in [1..21] ];

Mathematica

CoefficientList[Series[(1 - x)/(1 - 8*x + 14*x^2), {x,0,50}], x] (* or *) LinearRecurrence[{8,-14}, {1,7}, 50] (* G. C. Greubel, Sep 09 2017 *)

PARI

x='x+O('x^50); Vec((1-x)/(1-8*x+14*x^2)) \\ G. C. Greubel, Sep 09 2017

Formula

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

G.f.: (1-x)/(1-8*x+14*x^2).

E.g.f.: (cosh(sqrt(2)*x) + (3*sqrt(2)/2)*sinh(sqrt(2)*x))*exp(4*x). - G. C. Greubel, Sep 09 2017