A191566 a(n) = 7*a(n-1) + (-1)^n*6*2^(n-1).

1, 1, 19, 109, 811, 5581, 39259, 274429, 1921771, 13450861, 94159099, 659107549, 4613765131, 32296331341, 226074368539, 1582520481469, 11077643566891, 77543504575021, 542804532811579, 3799631728108189

Offset: 0

Author

Paul Curtz, Jun 06 2011

Keywords

• nonn
• easy

Comments

A007283(n) = 3*2^n. A091629(n+1) = 6*2^n.

a(n) + a(n+2) = 10 * (b(n) = 2, 11, 83, 569, 4007, ...).

b(n+1) = 7*b(n) - (-1)^n*3*2^n.

Inverse binomial transform of A007613(n).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Index entries for linear recurrences with constant coefficients, signature (5,14).

Programs

Magma

[(7^n+2*(-2)^n)/3: n in [0..30]]; // Vincenzo Librandi, Jun 07 2011

Mathematica

LinearRecurrence[{5,14},{1,1},40] (* Harvey P. Dale, Mar 01 2017 *)
CoefficientList[Series[(1 - 4*x)/(1 - 5*x - 14*x^2), {x, 0, 20}], x] (* Stefano Spezia, Sep 12 2018 *)

PARI

a(n)=(7^n+2*(-2)^n)/3 \\ Charles R Greathouse IV, Jun 06 2011

Formula

a(n+1) - a(n) = 18 * (0 followed by A053573(n)).

a(n) = (7^n + 2*(-2)^n)/3. - Charles R Greathouse IV, Jun 06 2011

G.f.: (1-4*x)/(1 - 5*x - 14*x^2). - Bruno Berselli, Jun 07 2011

a(n) = 5*a(n-1) + 14*a(n-2).