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 A020737 Pisot sequence L(5,9). 10
 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 (list; graph; refs; listen; history; text; internal format)
 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) = 3a(n-1) - 2a(n-2). G.f.: -(6*x-5) / ((x-1)*(2*x-1)). - Colin Barker, Jun 21 2014 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. 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 STATUS approved

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Last modified January 20 21:36 EST 2019. Contains 319336 sequences. (Running on oeis4.)