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A164908 a(n) = (3*4^n-0^n)/2. 4
1, 6, 24, 96, 384, 1536, 6144, 24576, 98304, 393216, 1572864, 6291456, 25165824, 100663296, 402653184, 1610612736, 6442450944, 25769803776, 103079215104, 412316860416, 1649267441664, 6597069766656, 26388279066624 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A164907. Inverse binomial transform of A057651.

Partial sums are in A083420.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = 4*a(n-1) for n > 1; a(0) = 1, a(1) = 6.

G.f.: (1+2*x)/(1-4*x).

MATHEMATICA

a[n_]:=(MatrixPower[{{2, 2}, {2, 2}}, n].{{2}, {1}})[[2, 1]]; Table[a[n], {n, 0, 40}] [From Vladimir Joseph Stephan Orlovsky, Feb 20 2010]

Join[{1}, (3*4^Range[25])/2] (* or *) Join[{1}, NestList[4#&, 6, 25]] (* Harvey P. Dale, Feb 14 2012 *)

PROG

(MAGMA) [ (3*4^n-0^n)/2: n in [0..22] ];

CROSSREFS

Equals 1 followed by A002023 (6*4^n). Essentially the same as A084509.

Cf. A164907, A057651, A083420 (2*4^n-1).

Sequence in context: A079839 A242432 A169759 * A002023 A037505 A048179

Adjacent sequences:  A164905 A164906 A164907 * A164909 A164910 A164911

KEYWORD

nonn

AUTHOR

Klaus Brockhaus, Aug 31 2009

STATUS

approved

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Last modified August 29 08:09 EDT 2014. Contains 246187 sequences.