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A048578
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Pisot sequence L(3,5).
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4
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3, 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; internal format)
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OFFSET
| 0,1
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REFERENCES
| G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence Sequences, Amer. Math. Soc., 2003; see esp. p. 255.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
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FORMULA
| a(n) = 2^(n+1)+1. a(n) = 3*a(n-1) - 2*a(n-2).
O.g.f.: -1/(-1+x)-2/(-1+2*x) . - R. J. Mathar, Nov 23 2007
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MAPLE
| a:=n->sum(binomial(n, k)+binomial(k, n), k=0..n): seq(a(n), n=1..33); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 29 2007
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PROG
| (Other) sage: [gaussian_binomial(n, 1, 2)+2 for n in xrange(1, 34)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 31 2009]
(MAGMA) [2^(n+1)+1 : n in [0..40]]; // Vincenzo Librandi, Sep 01 2011
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CROSSREFS
| Essentially the same as A000079.
Subsequence of A000051. See A008776 for definitions of Pisot sequences.
Sequence in context: A135728 A083318 A127904 * A087312 A099170 A018095
Adjacent sequences: A048575 A048576 A048577 * A048579 A048580 A048581
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KEYWORD
| nonn,easy
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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