A020737 Pisot sequence L(5,9).

5, 9, 17, 33, 65, 129, 257, 513, 1025, 2049, 4097, 8193, 16385, 32769, 65537, 131073, 262145, 524289, 1048577, 2097153, 4194305, 8388609, 16777217, 33554433, 67108865, 134217729, 268435457, 536870913, 1073741825, 2147483649, 4294967297, 8589934593

Offset

0,1

Comments

An Engel expansion of 1/2 to the base 2 as defined in A181565, with the associated series expansion 1/2 = 2/5 + 2^2/(5*9) + 2^3/(5*9*17) + 2^4/(5*9*17*33) + ... . - Peter Bala, Oct 28 2013

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..238

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

Formula

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

a(n) = 3*a(n-1) - 2*a(n-2).

G.f.: -(6*x-5) / ((x-1)*(2*x-1)). - Colin Barker, Jun 21 2014

E.g.f.: exp(x)*(1 + 4*exp(x)). - Stefano Spezia, Oct 08 2022

Mathematica

LinearRecurrence[{3, -2}, {5, 9}, 40] (* Harvey P. Dale, Jun 10 2015 *)

Prog

(Magma) [2^(n+2)+1: n in [0..40] ]; // Vincenzo Librandi, Apr 28 2011
(PARI) a(n)=2^(n+2)+1 \\ Charles R Greathouse IV, Jun 05 2013
(PARI) Vec(-(6*x-5)/((x-1)*(2*x-1)) + O(x^100)) \\ Colin Barker, Jun 21 2014

Crossrefs

Subsequence of A000051. See A008776 for definitions of Pisot sequences.

Cf. A083575, A083683, A083686, A083705, A168596, A181565, A195744.

Sequence in context: A059743 A000322 A205539 * A262452 A147401 A062536

Adjacent sequences: A020734 A020735 A020736 * A020738 A020739 A020740

Keyword

nonn,easy

Author

David W. Wilson

Status

approved