A175976 a(n) = 4^n - 3*n + 1.

2, 2, 11, 56, 245, 1010, 4079, 16364, 65513, 262118, 1048547, 4194272, 16777181, 67108826, 268435415, 1073741780, 4294967249, 17179869134, 68719476683, 274877906888, 1099511627717, 4398046511042, 17592186044351, 70368744177596, 281474976710585, 1125899906842550

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..250

Index entries for linear recurrences with constant coefficients, signature (6,-9,4).

Formula

G.f.: (-2+10*x-17*x^2)/((4*x-1)*(x-1)^2).

From Bruno Berselli, Nov 04 2010: (Start)

a(n) - 6*a(n-1) + 9*a(n-2) - 4*a(n-3) = 0 for n > 2.

a(n) = A158879(n) - A131098(n+1) (n > 0). (End)

E.g.f.: exp(x)*(1 - 3*x + exp(3*x)). - Elmo R. Oliveira, Mar 07 2025

Example

a(1)=4-3+1=2. a(2)=16-6+1=11.

Maple

A175976 := proc(n) 4^n-3*n+1 ; end proc:

Mathematica

Table[4^n-3n+1, {n, 0, 30}] (* or *) LinearRecurrence[{6, -9, 4}, {2, 2, 11}, 30] (* Harvey P. Dale, Jul 07 2013 *)

Prog

(Magma) [4^n-3*n+1: n in [0..30]]; // Vincenzo Librandi, Mar 20 2014

Crossrefs

Cf. A131098, A158879.

Sequence in context: A184237 A069648 A275869 * A095215 A264712 A217094

Adjacent sequences: A175973 A175974 A175975 * A175977 A175978 A175979

Keyword

nonn,easy,changed

Author

Vincenzo Librandi, Nov 02 2010

Extensions

G.f., program and link to recurrences from R. J. Mathar, Nov 03 2010

Status

approved