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A126646
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a(n) = 2^(n+1) - 1.
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30
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1, 3, 7, 15, 31, 63, 127, 255, 511, 1023, 2047, 4095, 8191, 16383, 32767, 65535, 131071, 262143, 524287, 1048575, 2097151, 4194303, 8388607, 16777215, 33554431, 67108863, 134217727, 268435455, 536870911, 1073741823, 2147483647
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OFFSET
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0,2
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COMMENTS
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a(n) is the number of integers k less than 10^n such that the decimal representation of k lacks the digits 1,2,3,4,5,6 and 7 and at least one of the digits 8,9.
Partial sums of the powers of 2 (A000079).
a(n-1)^2 + a(n) is a(2n)+1, a square. Examples: 3^2 + 7 = 16; 7^2 + 15 = 64; 15^2 + 31 = 256. - Vincenzo Librandi and Ralf Stephan, Nov 23 2010
a(n) is the number of elements (all m-dimensional faces) in an n-dimensional simplex (0 <= m <= n). - Sergey Pavlov, Aug 15 2015
A261461(a(n)) != A261922(a(n)). - Reinhard Zumkeller, Sep 17 2015
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..1000
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
Jerry Metzger and Thomas Richards, A Prisoner Problem Variation, Journal of Integer Sequences, Vol. 18 (2015), Article 15.2.7.
Wikipedia, Simplex Elements (see last column of table).
Index entries for linear recurrences with constant coefficients, signature (3,-2).
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FORMULA
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G.f.: 1/ ( (1-2*x)*(1-x) ). - R. J. Mathar, Dec 02 2013
a(n) = 3*a(n-1) - 2*a(n-2), n > 1. - Wesley Ivan Hurt, Aug 21 2015
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EXAMPLE
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a(8) = 2^9 - 1 = 511.
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MAPLE
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A126646:=n->2*2^n-1; seq(A126646(n), n=0..50); # Wesley Ivan Hurt, Dec 02 2013
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MATHEMATICA
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Table[2^(n + 1) - 1, {n, 0, 50}] (* Wesley Ivan Hurt, Dec 02 2013 *)
LinearRecurrence[{3, -2}, {1, 3}, 40] (* Harvey P. Dale, Mar 23 2018 *)
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PROG
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(PARI) first(m)=vector(m, i, i--; 2^(i+1)-1) /* Anders Hellström, Aug 19 2015 */
(MAGMA) [2^(n+1)-1: n in [0.. 35]]; // Vincenzo Librandi, Aug 20 2015
(Haskell)
a126646 = (subtract 1) . (2 ^) . (+ 1)
a126646_list = iterate ((+ 1) . (* 2)) 1
-- Reinhard Zumkeller, Sep 17 2015
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CROSSREFS
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Essentially the same as A000225.
Cf. A125630, A125945, A125947, A125948, A125940, A125909, A125908, A125880, A125897, A125904, A125858.
Cf. A000079, A168604.
Cf. A261461, A261922.
Sequence in context: A336700 A097002 A060152 * A000225 A225883 A255047
Adjacent sequences: A126643 A126644 A126645 * A126647 A126648 A126649
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KEYWORD
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nonn,easy
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AUTHOR
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Aleksandar M. Janjic and Milan Janjic, Feb 08 2007, Feb 13 2007
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STATUS
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approved
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