A036543 a(n) = T(3,n), array T given by A048471.

1, 9, 33, 105, 321, 969, 2913, 8745, 26241, 78729, 236193, 708585, 2125761, 6377289, 19131873, 57395625, 172186881, 516560649, 1549681953, 4649045865, 13947137601, 41841412809, 125524238433, 376572715305, 1129718145921

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Links

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

Crossrefs

n-th difference of a(n), a(n-1), ..., a(0) is 2^(n+2) for n=1, 2, 3, ...

Cf. A146541 (inv. bin. transf.)

Programs

Magma

[4*3^n-3: n in [0..30]]; // Vincenzo Librandi, Nov 11 2011

Mathematica

4*3^Range[0,25]-3 (* or *) LinearRecurrence[{4,-3},{1,9},25] (* Harvey P. Dale, Aug 16 2011 *)

PARI

vector(30, n, n--; 4*3^n-3) \\ G. C. Greubel, Nov 23 2018

Sage

[4*3^n-3 for n in range(30)] # G. C. Greubel, Nov 23 2018

Formula

Binomial transform of A084242. Second binomial transform of periodic sequence A010688. - Paul Barry, May 23 2003

From Paul Barry, May 23 2003: (Start)

a(n) = 4*3^n - 3;

G.f.: (1+5*x)/((1-x)*(1-3*x));

E.g.f.: 4*exp(3*x) - 3*exp(x). (End)

a(n) = 4*a(n-1) - 3*a(n-2); a(0)=1, a(1)=9. - Harvey P. Dale, Aug 16 2011

a(n) = 3*a(n-1) + 6. - Vincenzo Librandi, Nov 11 2011

a(n) = A171498(n) - 2. - Philippe Deléham, Apr 13 2013