|
Search: id:A074872
|
|
|
| A074872 |
|
Inverse BinomialMean transform of the Fibonacci sequence A000045 (with the initial 0 omitted). |
|
+0
3
|
|
| 1, 1, 5, 5, 25, 25, 125, 125, 625, 625, 3125, 3125, 15625, 15625, 78125, 78125, 390625, 390625, 1953125, 1953125, 9765625, 9765625, 48828125, 48828125, 244140625, 244140625, 1220703125, 1220703125, 6103515625, 6103515625
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
See A075271 for the definition of the BinomialMean transform.
The inverse binomial transform of 2^n*c(n+1), where c(n) is the solution to c(n)=c(n-1)+kc(n-2), a(0)=0,a(1)=1 is 1,1,4k+1,4k+1,(4k+1)^2,... - Paul Barry (pbarry(AT)wit.ie), Feb 12 2004
|
|
FORMULA
|
a(n)=5^Floor((n-1)/2). a(1)=1, a(2)=1, and, for n>2, a(n)=5*a(n-2).
G.f.: (1+x)/(1-5x^2); a(n)=(1/(2sqrt(5))((1+sqrt(5))(sqrt(5))^n-(1-sqrt(5))(-sqrt(5))^n)). Inverse binomial transform of A063727 (2^n*Fib(n+1)). - Paul Barry (pbarry(AT)wit.ie), Feb 12 2004
|
|
CROSSREFS
|
Adjacent sequences: A074869 A074870 A074871 this_sequence A074873 A074874 A074875
Sequence in context: A090936 A071340 A056451 this_sequence A038247 A093643 A130220
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
John W. Layman (layman(AT)math.vt.edu), Sep 12 2002
|
|
|
Search completed in 0.002 seconds
|
