login
A081631
a(n) = 2*2^n - (-2)^n.
5
1, 6, 4, 24, 16, 96, 64, 384, 256, 1536, 1024, 6144, 4096, 24576, 16384, 98304, 65536, 393216, 262144, 1572864, 1048576, 6291456, 4194304, 25165824, 16777216, 100663296, 67108864, 402653184, 268435456, 1610612736, 1073741824
OFFSET
0,2
COMMENTS
Binomial transform of A081630. Inverse binomial transform of A081632.
FORMULA
G.f.: (1+6*x)/((1-2*x)*(1+2*x)).
E.g.f.: 2*exp(2*x)-exp(-2*x).
MATHEMATICA
CoefficientList[Series[(1 + 6 x) / ((1 - 2 x) (1 + 2 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Aug 10 2013 *)
LinearRecurrence[{0, 4}, {1, 6}, 40] (* or *) With[{nn=20}, Riffle[ NestList[ 4#&, 1, nn], NestList[4#&, 6, nn]]] (* Harvey P. Dale, Aug 04 2019 *)
PROG
(Magma) [2*2^n-(-2)^n: n in [0..40]]; // Vincenzo Librandi, Aug 10 2013
(PARI) a(n)=2*2^n-(-2)^n \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
Sequence in context: A169689 A328757 A061592 * A137174 A129886 A133837
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Mar 26 2003
STATUS
approved