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A147590
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Numbers whose binary representation is the concatenation of 2n-1 digits 1 and n-1 digits 0.
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9
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1, 14, 124, 1016, 8176, 65504, 524224, 4194176, 33554176, 268434944, 2147482624, 17179867136, 137438949376, 1099511619584, 8796093005824, 70368744144896, 562949953355776, 4503599627239424, 36028797018701824, 288230376151187456
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OFFSET
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1,2
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COMMENTS
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a(n) is the number whose binary representation is A147589(n).
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LINKS
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Nathaniel Johnston, Table of n, a(n) for n = 1..500
Index entries for linear recurrences with constant coefficients, signature (10,-16).
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FORMULA
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a(n) = A147537(n)/2.
From R. J. Mathar, Jul 13 2009: (Start)
a(n) = 8^n/4 - 2^(n-1) = A083332(2n-2).
a(n) = 10*a(n-1) - 16*a(n-2).
G.f.: x*(1+4*x)/((1-2*x)*(1-8*x)). (End)
From César Aguilera, Jul 26 2019: (Start)
Lim_{n->infinity} a(n)/a(n-1) = 8;
a(n)/a(n-1) = 8 + 6/A083420(n). (End)
E.g.f.: (1/4)*(exp(2*x)*(-2 + exp(6*x)) + 1). - Stefano Spezia, Aug 05 2019
a(n) = A020540(n - 1)/4. - Jon Maiga, Aug 05 2019
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EXAMPLE
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1_10 is 1_2;
14_10 is 1110_2;
124_10 is 1111100_2;
1016_10 is 1111111000_2.
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MAPLE
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seq(8^n/4-2^(n-1), n=1..25); # Nathaniel Johnston, Apr 30 2011
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MATHEMATICA
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LinearRecurrence[{10, -16}, {1, 14}, 30] (* Harvey P. Dale, Oct 10 2014 *)
Table[8^n / 4 - 2^(n - 1), {n, 25}] (* Vincenzo Librandi, Jul 27 2019 *)
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PROG
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(MAGMA) [8^n/4-2^(n-1): n in [1..25]]; // Vincenzo Librandi, Jul 27 2019
(PARI) vector(25, n, 2^(n-2)*(4^n-2)) \\ G. C. Greubel, Jul 27 2019
(Sage) [2^(n-2)*(4^n-2) for n in (1..25)] # G. C. Greubel, Jul 27 2019
(GAP) List([1..25], n-> 2^(n-2)*(4^n-2)); # G. C. Greubel, Jul 27 2019
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CROSSREFS
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Cf. A020540, A138118, A147537, A147589.
Sequence in context: A167567 A188411 A125377 * A167602 A212234 A155637
Adjacent sequences: A147587 A147588 A147589 * A147591 A147592 A147593
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KEYWORD
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base,easy,nonn
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AUTHOR
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Omar E. Pol, Nov 08 2008
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EXTENSIONS
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More terms from R. J. Mathar, Jul 13 2009
Typo in a(12) corrected by Omar E. Pol, Jul 20 2009
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STATUS
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approved
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