A085280 Expansion of (1-4x+x^2)/((1-x)(1-3x)(1-4x)).

1, 4, 14, 48, 166, 584, 2094, 7648, 28406, 107064, 408574, 1575248, 6123846, 23963944, 94261454, 372262848, 1474702486, 5855763224, 23293912734, 92788230448, 369990660326, 1476475856904, 5895443074414, 23550391238048

Offset: 0

Author

Paul Barry, Jun 25 2003

Keywords

• nonn
• easy

Comments

Binomial transform of A085279.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Index entries for linear recurrences with constant coefficients, signature (8,-19,12).

Programs

Magma

[3^n+4^n/3-1/3: n in [0..30]]; // Vincenzo Librandi, May 26 2013

Mathematica

Table[(3^n + 4^n/3 - 1/3), {n, 0, 30}] (* Vincenzo Librandi, May 26 2013 *)
CoefficientList[Series[(1-4x+x^2)/((1-x)(1-3x)(1-4x)),{x,0,30}],x] (* Harvey P. Dale, Jan 02 2021 *)

Formula

a(n) = 3^n+4^n/3-1/3.