A155155 a(n) = 2*(10*3^n - 1).

18, 58, 178, 538, 1618, 4858, 14578, 43738, 131218, 393658, 1180978, 3542938, 10628818, 31886458, 95659378, 286978138, 860934418, 2582803258, 7748409778, 23245229338, 69735688018, 209207064058, 627621192178, 1882863576538

Offset: 0

Author

Paul Curtz, Jan 21 2009

Keywords

• nonn
• easy
• less

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-3).

Crossrefs

Cf. A003462, A048473.

Programs

Magma

[2*(10*3^n-1): n in [0..30]]; // Vincenzo Librandi, Aug 07 2011

Maple

seq(2*(10*3^n -1), n=0..30); # G. C. Greubel, Mar 20 2021

Mathematica

2*(10*3^Range[0,30] -1) (* G. C. Greubel, Mar 20 2021 *)

Sage

[2*(10*3^n - 1) for n in (0..30)] # G. C. Greubel, Mar 20 2021

Formula

a(n) = 4*a(n-1) - 3*a(n-2).

G.f.: ( 18 - 14*x ) / ( (1-x)*(1-3*x) ).

a(n) = 10*A048473(n) + 8 = A048473(n) + A048473(n+2).

a(n) = 3*a(n-1) - a(n-2) + 3*a(n-3) + 8.

From G. C. Greubel, Mar 20 2021: (Start)

a(n) = 18*A003462(n+1) - 14*A003462(n).

E.g.f.: 2*( 10*exp(3*x) - exp(x) ). (End)

a(n) = 2 * A198645(n). - Joerg Arndt, Mar 21 2021