A133464 a(3n)=4^n, a(3n+1)=2*4^n, a(3n+2)=3*4^n.
1, 2, 3, 4, 8, 12, 16, 32, 48, 64, 128, 192, 256, 512, 768, 1024, 2048, 3072, 4096, 8192, 12288, 16384, 32768, 49152, 65536, 131072, 196608, 262144, 524288, 786432, 1048576, 2097152, 3145728, 4194304, 8388608, 12582912, 16777216, 33554432
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (0,0,4).
Programs
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Mathematica
LinearRecurrence[{0,0,4},{1,2,3},40] (* Harvey P. Dale, Jun 07 2012 *) -
PARI
a(n)=4^(n\3)*(n%3+1) \\ Charles R Greathouse IV, Oct 07 2015
Formula
O.g.f.: -(1+2*x+3*x^2)/(-1+4*x^3) . 2*a(n)-a(n+1) = abs(A117902(n+1)). - R. J. Mathar, Nov 30 2007
From Reinhard Zumkeller, May 26 2008: (Start)
a(n+1) = a(n) + a(n - n mod 3).
a(n) = A140740(n+3,3). (End)
Sum_{n>=0} 1/a(n) = 22/9. - Amiram Eldar, Jan 21 2022
Extensions
Edited by R. J. Mathar, Nov 30 2007
More terms from Reinhard Zumkeller, May 26 2008