A212323 a(n) = 3^n - Fibonacci(n).

1, 2, 8, 25, 78, 238, 721, 2174, 6540, 19649, 58994, 177058, 531297, 1594090, 4782592, 14348297, 43045734, 129138566, 387417905, 1162257286, 3486777636, 10460342257, 31381041898, 94143150170, 282429490113, 847288534418, 2541865706936, 7625597288569

Offset: 0

Author

Bruno Berselli, May 09 2012

Keywords

• nonn
• easy

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-2,-3).

Crossrefs

Cf. A000045, A000244, A099036, A212262.

Programs

Magma

[3^n-Fibonacci(n): n in [0..27]];

Mathematica

Table[3^n - Fibonacci[n], {n, 0, 27}]
LinearRecurrence[{4,-2,-3},{1,2,8},30] (* Harvey P. Dale, Dec 08 2023 *)

PARI

for(n=0, 27, print1(3^n-fibonacci(n)", "));

Formula

G.f.: (1 - 2*x + 2*x^2)/((1 - 3*x)*(1 - x - x^2)).