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A176691 a(n) = 2^n + 2*n + 1. 6
2, 5, 9, 15, 25, 43, 77, 143, 273, 531, 1045, 2071, 4121, 8219, 16413, 32799, 65569, 131107, 262181, 524327, 1048617, 2097195, 4194349, 8388655, 16777265, 33554483, 67108917, 134217783, 268435513, 536870971, 1073741885, 2147483711 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The subsequence of primes in this sequence is A163115.

LINKS

Table of n, a(n) for n=0..31.

Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

FORMULA

a(n) = 2^n + 2*n + 1 = A000079(n) + A005843(n) + 1 = A000051(n) + A005843(n).

From R. J. Mathar, Apr 28 2010: (Start)

a(n) = +4*a(n-1) -5*a(n-2) +2*a(n-3).

G.f.: ( -2+3*x+x^2 ) / ( (2*x-1)*(x-1)^2 ). (End)

MATHEMATICA

Table[2^n+2*n+1, {n, 0, 60}] (* Vladimir Joseph Stephan Orlovsky, Feb 15 2011 *)

LinearRecurrence[{4, -5, 2}, {2, 5, 9}, 40] (* Vincenzo Librandi, Aug 12 2015 *)

PROG

(PARI) vector(40, n, n--; 2^n + 2*n + 1) \\ Michel Marcus, Aug 12 2015

(MAGMA) [2^n + 2*n + 1: n in [0..40]]; // Vincenzo Librandi, Aug 12 2015

CROSSREFS

Cf. A000051, A005126, A194455, A000079, A000290, A005843.

Sequence in context: A100287 A007176 A267757 * A274355 A054253 A045649

Adjacent sequences:  A176688 A176689 A176690 * A176692 A176693 A176694

KEYWORD

nonn,easy

AUTHOR

Jonathan Vos Post, Apr 23 2010

EXTENSIONS

Corrected (one 1048617 replaced by 2097195) by R. J. Mathar, Apr 28 2010

STATUS

approved

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Last modified May 22 19:31 EDT 2017. Contains 286885 sequences.