A081654 a(n) = 2*4^n - 0^n.
1, 8, 32, 128, 512, 2048, 8192, 32768, 131072, 524288, 2097152, 8388608, 33554432, 134217728, 536870912, 2147483648, 8589934592, 34359738368, 137438953472, 549755813888, 2199023255552, 8796093022208, 35184372088832
Offset: 0
Examples
a(0) = 2*4^0 - 0^0 = 2 - 1 = 1 (use 0^0 = 1).
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index to divisibility sequences
- Index entries for linear recurrences with constant coefficients, signature (4).
Programs
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Magma
[2*4^n-0^n: n in [0..30]]; // Vincenzo Librandi, Aug 10 2013
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Mathematica
CoefficientList[Series[(1 + 4 x) / (1 - 4 x), {x, 0, 40}], x] (* Vincenzo Librandi, Aug 10 2013 *) -
PARI
a(n)=2*4^n-0^n \\ Charles R Greathouse IV, Apr 09 2012
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PARI
x='x+O('x^100); Vec((1+4*x)/(1-4*x)) \\ Altug Alkan, Dec 14 2015
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
Comments