|
Search: id:A112387
|
|
|
| A112387 |
|
a(1)=1, a(2)=2, a(n)= 2^(n/2) if even and a(n-1)-a(n-2) if odd. |
|
+0
1
|
|
| 1, 2, 1, 4, 3, 8, 5, 16, 11, 32, 21, 64, 43, 128, 85, 256, 171, 512, 341, 1024, 683, 2048, 1365, 4096, 2731, 8192, 5461, 16384, 10923, 32768, 21845, 65536, 43691, 131072, 87381, 262144, 174763, 524288, 349525, 1048576, 699051, 2097152, 1398101
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
This sequence originated from the Fibonacci sequence, but instead of adding the last two terms, you get the average. Example, if you have the initial condition a(1)=x and a(2)=y, a(3)=(x+y)/2, a(4)=(x+3y)/4, a(5)=(3x+5y)/8, a(6)=(5x+11y)/16 and so on and so forth. I used the coefficients of x and y as well as the denominator.
|
|
FORMULA
|
a(n)=2^(n/2) if n is even, a(n)=a(n-1)-a(n-2) if n is odd and with initial condition of a(1)=1. The limit of a(n)/a(n+1) as n approaches infinity oscillates at a value of 3/2 and 1/3.
a(2n)=A000079(n), a(2n-1)=A001045(n).
|
|
MATHEMATICA
|
a[1] = 1; a[2] = 2; a[n_] := a[n] = If[ EvenQ[n], 2^(n/2), a[n - 1] - a[n - 2]]; Array[a, 43] (* Robert G. Wilson v *)
|
|
CROSSREFS
|
Sequence in context: A128280 A106625 A008347 this_sequence A076077 A087787 A100818
Adjacent sequences: A112384 A112385 A112386 this_sequence A112388 A112389 A112390
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Edwin F. Sampang (efs_files(AT)yahoo.com), Dec 05 2005
|
|
EXTENSIONS
|
Edited and extended by Robert G. Wilson v (rgwv(at)rgwv.com), Dec 05 2005
|
|
|
Search completed in 0.002 seconds
|
