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 A016152 a(n) = 4^(n-1)*(2^n-1). 8
 0, 1, 12, 112, 960, 7936, 64512, 520192, 4177920, 33488896, 268173312, 2146435072, 17175674880, 137422176256, 1099444518912, 8795824586752, 70367670435840, 562945658454016, 4503582447501312, 36028728299487232 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Numbers whose binary representation is the concatenation of n digits 1 and 2(n-1) digits 0, for n>0. (See A147816.) - Omar E. Pol, Nov 13 2008 a(n) is the number of lattices L in Z^n such that the quotient group Z^n / L is C_8. - Álvar Ibeas, Nov 29 2015 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..140 Index entries for linear recurrences with constant coefficients, signature (12,-32). FORMULA From Barry E. Williams, Jan 17 2000: (Start) a(n) = ((8^(n+1)) - 4^(n+1))/4. a(n) = 12a(n-1) - 32a(n-2), n>0; a(0)=1. (End) a(n) = (4^(n-1))*Stirling2(n+1, 2), n>=0, with Stirling2(n, m)=A008277(n, m). a(n) = -4^(n-1) + 2*8^(n-1). E.g.f. for a(n+1), n>=0: d^2/dx^2((((exp(4*x)-1)/4)^2)/2!) = -exp(4*x) + 2*exp(8*x). G.f.: x/((1-4*x)*(1-8*x)). ((6+sqrt4)^n - (6-sqrt4)^n)/4 in Fibonacci form. Offset 1. a(3)=112. - Al Hakanson (hawkuu(AT)gmail.com), Dec 31 2008 a(n) + A160873(n) + A006096(n) = A006096(n+2), for n > 2. - Álvar Ibeas, Nov 29 2015 Sum_{n>0} 1/a(n) = 4*E - 16/3, where E is the Erdős-Borwein constant (A065442). - Peter McNair, Dec 19 2022 MATHEMATICA Table[4^(n - 1) (2^n - 1), {n, 0, 19}] (* Michael De Vlieger, Nov 30 2015 *) PROG (Sage) [lucas_number1(n, 12, 32) for n in range(0, 20)] # Zerinvary Lajos, Apr 27 2009 (Magma) [4^(n-1)*(2^n-1): n in [0..40]]; // Vincenzo Librandi, Apr 26 2011 (PARI) a(n)=4^(n-1)*(2^n-1) \\ Charles R Greathouse IV, Oct 07 2015 (PARI) x='x+O('x^100); concat(0, Vec(x/((1-4*x)*(1-8*x)))) \\ Altug Alkan, Dec 04 2015 CROSSREFS Second column of triangle A075499. Cf. A019677, A147538, A147816. Cf. A065442. Sequence in context: A225189 A044725 A265948 * A089700 A290742 A268767 Adjacent sequences: A016149 A016150 A016151 * A016153 A016154 A016155 KEYWORD nonn,easy AUTHOR N. J. A. Sloane STATUS approved

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Last modified September 25 12:47 EDT 2023. Contains 365644 sequences. (Running on oeis4.)