A257970 a(1) = 1, a(2) = 2, a(3) = 5; thereafter a(n) = 2 * Sum_{k=1..n-1} a(k).

1, 2, 5, 16, 48, 144, 432, 1296, 3888, 11664, 34992, 104976, 314928, 944784, 2834352, 8503056, 25509168, 76527504, 229582512, 688747536, 2066242608, 6198727824, 18596183472, 55788550416, 167365651248, 502096953744, 1506290861232, 4518872583696, 13556617751088

Offset

1,2

Links

Table of n, a(n) for n=1..29.

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

Formula

G.f.: -x*(x+1)*(x-1)^2/(3*x-1). [Corrected by Vincenzo Librandi, May 25 2015]

a(n) = 3*a(n-1) for n>=5.

a(n) = 16*3^(n-4) for n>=4.

Mathematica

CoefficientList[Series[(x + 1) (x - 1)^2/(1 - 3 x), {x, 0, 33}], x] (* Vincenzo Librandi, May 25 2015 *)
Join[{1, 2, 5}, NestList[3#&, 16, 30]] (* Harvey P. Dale, Dec 20 2018 *)

Prog

(Magma) [1, 2, 5] cat [16*3^(n-4): n in [4..50]]; // Vincenzo Librandi, May 25 2015

Crossrefs

Sequence in context: A148378 A394236 A148379 * A148380 A210696 A005497

Adjacent sequences: A257967 A257968 A257969 * A257971 A257972 A257973

Keyword

nonn,easy,less

Author

Harry Farrar, May 15 2015

Status

approved