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 A147590 Numbers whose binary representation is the concatenation of 2n-1 digits 1 and n-1 digits 0. 9
 1, 14, 124, 1016, 8176, 65504, 524224, 4194176, 33554176, 268434944, 2147482624, 17179867136, 137438949376, 1099511619584, 8796093005824, 70368744144896, 562949953355776, 4503599627239424, 36028797018701824, 288230376151187456 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) is the number whose binary representation is A147589(n). LINKS Nathaniel Johnston, Table of n, a(n) for n = 1..500 Index entries for linear recurrences with constant coefficients, signature (10,-16). FORMULA 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 EXAMPLE 1_10 is 1_2;     14_10 is 1110_2;    124_10 is 1111100_2;   1016_10 is 1111111000_2. MAPLE seq(8^n/4-2^(n-1), n=1..25); # Nathaniel Johnston, Apr 30 2011 MATHEMATICA 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 *) PROG (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 CROSSREFS Cf. A020540, A138118, A147537, A147589. Sequence in context: A167567 A188411 A125377 * A167602 A212234 A155637 Adjacent sequences:  A147587 A147588 A147589 * A147591 A147592 A147593 KEYWORD base,easy,nonn AUTHOR Omar E. Pol, Nov 08 2008 EXTENSIONS More terms from R. J. Mathar, Jul 13 2009 Typo in a(12) corrected by Omar E. Pol, Jul 20 2009 STATUS approved

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Last modified August 18 19:12 EDT 2022. Contains 356215 sequences. (Running on oeis4.)