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A158879 4^n + n. 9
1, 5, 18, 67, 260, 1029, 4102, 16391, 65544, 262153, 1048586, 4194315, 16777228, 67108877, 268435470, 1073741839, 4294967312, 17179869201, 68719476754, 274877906963, 1099511627796, 4398046511125, 17592186044438, 70368744177687 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..300

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

FORMULA

G.f.: (-1+x+3*x^2)/((4*x-1)*(x-1)^2). - R. J. Mathar, Mar 29 2009

a(n) = 6*a(n-1) -9*a(n-2) +4a(n-3). - R. J. Mathar, Mar 29 2009

EXAMPLE

a(0)=4^0+0 = 1, a(1)=4^1+1 = 5, a(2)=4^2+2 = 18, a(3)=4^3+3 = 67, ...

MATHEMATICA

Table[4^n+n, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, May 19 2011 *)

CoefficientList[Series[(-1 + x + 3 x^2) / ((4 x - 1) (x - 1)^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jun 16 2013 *)

LinearRecurrence[{6, -9, 4}, {1, 5, 18}, 30] (* Harvey P. Dale, Jun 02 2016 *)

PROG

(MAGMA) [4^n+n: n in [0..30]]; // Vincenzo Librandi, Jun 16 2013

(PARI) a(n)=4^n+n \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Cf. A006127, A104743, A104745, A081552.

Sequence in context: A225015 A166677 A318062 * A322497 A279488 A199843

Adjacent sequences:  A158876 A158877 A158878 * A158880 A158881 A158882

KEYWORD

nonn,easy

AUTHOR

Philippe Deléham, Mar 28 2009

EXTENSIONS

Corrected typo in a(22) from R. J. Mathar, Mar 29 2009

STATUS

approved

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Last modified July 16 04:23 EDT 2019. Contains 325064 sequences. (Running on oeis4.)