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A048578 Pisot sequence L(3,5). 4
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; text; internal format)
OFFSET

0,1

REFERENCES

G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence Sequences, Amer. Math. Soc., 2003; see esp. p. 255.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

Josef Eschgfäller, Andrea Scarpante, Dichotomic random number generators, arXiv:1603.08500 [math.CO], 2016.

Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.

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

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

MAPLE

a:=n->sum(binomial(n, k)+binomial(k, n), k=0..n): seq(a(n), n=1..33); # Zerinvary Lajos, Apr 29 2007

MATHEMATICA

LinearRecurrence[{3, -2}, {3, 5}, 40] (* Harvey P. Dale, Sep 10 2017 *)

PROG

(Sage) [gaussian_binomial(n, 1, 2)+2 for n in xrange(1, 34)] # Zerinvary Lajos, May 31 2009

(MAGMA) [2^(n+1)+1 : n in [0..40]]; // Vincenzo Librandi, Sep 01 2011

(PARI) x='x+O('x^99); Vec(-1/(-1+x)-2/(-1+2*x)) \\ Altug Alkan, Mar 29 2016

CROSSREFS

Essentially the same as A000079.

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

Sequence in context: A135728 A083318 A127904 * A087312 A099170 A251705

Adjacent sequences:  A048575 A048576 A048577 * A048579 A048580 A048581

KEYWORD

nonn,easy

AUTHOR

David W. Wilson

STATUS

approved

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Last modified July 19 12:47 EDT 2018. Contains 312775 sequences. (Running on oeis4.)