A185940 a(n) = 1 - 2^(n+1) + 3^(n+2).

24, 74, 228, 698, 2124, 6434, 19428, 58538, 176124, 529394, 1590228, 4774778, 14332524, 43013954, 129074628, 387289418, 1161999324, 3486260114, 10459304628, 31378962458, 94138984524, 282421147874, 847271832228, 2541832273898, 7625530376124, 22876658237234

Offset: 1

Author

Amir H. Farrahi, Feb 06 2011

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-11,6).

Crossrefs

Cf. A000079, A000244, A066280.

Programs

Magma

[1 - 2^(n+1) + 3^(n+2): n in [1..40]]; // Vincenzo Librandi, Apr 05 2011

Maple

A185940:=n->1-2^(n+1)+3^(n+2): seq(A185940(n), n=1..40); # Wesley Ivan Hurt, Jul 23 2017

Mathematica

CoefficientList[Series[-2*x*(12 - 35*x + 24*x^2)/(-1 + 6*x - 11*x^2 + 6*x^3), {x,0,50}], x] (* or *) LinearRecurrence[{6, -11, 6}, {24, 74, 228}, 50] (* G. C. Greubel, Feb 25 2017 *)

PARI

x='x+O('x^50); Vec(-2*x*(12 - 35*x + 24*x^2) / (-1 + 6*x - 11*x^2 + 6*x^3)) \\ G. C. Greubel, Feb 25 2017

Formula

a(n) = 1 - A000079(n+1) + A000244(n+2)

From Alexander R. Povolotsky, Jan 07 2011: (Start)

G.f.: 2*x*(12 - 35*x + 24*x^2) / (1 - 6*x + 11*x^2 - 6*x^3)

a(n+2) = -6*a(n) + 5*a(n+1)+2. (End)

a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3). - G. C. Greubel, Feb 25 2017

E.g.f.: exp(x) - 2*exp(2*x) + 9*exp(3*x) - 8. - G. C. Greubel, Jul 23 2017

Extensions

Corrected and edited by Bruno Berselli, Apr 04 2011