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 A081654 a(n) = 2*4^n - 0^n. 8
 1, 8, 32, 128, 512, 2048, 8192, 32768, 131072, 524288, 2097152, 8388608, 33554432, 134217728, 536870912, 2147483648, 8589934592, 34359738368, 137438953472, 549755813888, 2199023255552, 8796093022208, 35184372088832 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform of A081632. Inverse binomial transform of A081655. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (4). FORMULA a(0)=1, a(n) = 2*4^n, n>0 G.f.: (1+4*x)/(1-4*x). E.g.f. 2*exp(4*x)-1. With interpolated zeros, this is 2^n - 0^n + (-2)^n. - Paul Barry, Sep 06 2003 a(n) = A081294(n+1), n>0. - R. J. Mathar, Sep 17 2008 For n>0, a(n) = 2 * (1 + 3^(n-1) + Sum{x=1..n-2}Sum{k=0..x-1}(binomial(x-1,k)*(3^(k+1) + 3^(n-x+k)))). - J. Conrad, Dec 10 2015 EXAMPLE a(0) = 2*4^0 - 0^0 = 2 - 1 = 1 (use 0^0 = 1). MATHEMATICA CoefficientList[Series[(1 + 4 x) / (1 - 4 x), {x, 0, 40}], x] (* Vincenzo Librandi, Aug 10 2013 *) PROG (PARI) a(n)=2*4^n-0^n \\ Charles R Greathouse IV, Apr 09 2012 (MAGMA) [2*4^n-0^n: n in [0..30]]; // Vincenzo Librandi, Aug 10 2013 *) (PARI) x='x+O('x^100); Vec((1+4*x)/(1-4*x)) \\ Altug Alkan, Dec 14 2015 CROSSREFS Cf. A000244 (3^n), A187093. Sequence in context: A269077 A183915 A325839 * A307004 A264280 A264390 Adjacent sequences:  A081651 A081652 A081653 * A081655 A081656 A081657 KEYWORD easy,nonn AUTHOR Paul Barry, Mar 26 2003 STATUS approved

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Last modified August 14 09:14 EDT 2020. Contains 336480 sequences. (Running on oeis4.)