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A171389 a(n) = 21*2^n - 1. 2
20, 41, 83, 167, 335, 671, 1343, 2687, 5375, 10751, 21503, 43007, 86015, 172031, 344063, 688127, 1376255, 2752511, 5505023, 11010047, 22020095, 44040191, 88080383, 176160767, 352321535, 704643071, 1409286143, 2818572287 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (3,-2).

FORMULA

a(n+1) = 2*a(n) + 1.

G.f.: (20-19*x)/((1-x)*(1-2*x)). - Vincenzo Librandi, Jul 06 2012

a(n) = 3*a(n-1) - 2*a(n-2). - Vincenzo Librandi, Jul 06 2012

a(n) + a(n-1)^2 = (a(n-1) + 1)^2. - Vincenzo Librandi, Jun 11 2014

MAPLE

A171389:=n->21*2^n-1; seq(A171389(n), n=0..40); # Wesley Ivan Hurt, Jun 11 2014

MATHEMATICA

CoefficientList[Series[(20-19*x)/((1-x)*(1-2*x)), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 06 2012 *)

PROG

(BASIC) for j = 0 to 30 : print str$((21*2^j)-1)+", "; : next j [Jeremy Gardiner, Oct 23 2011]

(MAGMA) I:=[20, 41]; [n le 2 select I[n] else 3*Self(n-1)-2*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Jul 06 2012

CROSSREFS

Cf. A086224, A175805.

Sequence in context: A041788 A041786 A195148 * A038639 A041792 A041794

Adjacent sequences:  A171386 A171387 A171388 * A171390 A171391 A171392

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Dec 07 2009

EXTENSIONS

Edited by Jon E. Schoenfield, Jun 23 2010

Offset changed to 0 and first formula corrected by Jeremy Gardiner, Oct 23 2011

STATUS

approved

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Last modified November 22 15:13 EST 2017. Contains 295089 sequences.