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

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-3).

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

Mathematica

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

Prog

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

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.)

Sequence in context: A031880 A231765 A220165 * A147269 A147123 A147107

Adjacent sequences: A036540 A036541 A036542 * A036544 A036545 A036546

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved