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A074872 Inverse BinomialMean transform of the Fibonacci sequence A000045 (with the initial 0 omitted). 11
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; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
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) + k*c(n-2), a(0)=0, a(1)=1 is 1, 1, 4k+1, 4k+1, (4k+1)^2, ... - Paul Barry, Feb 12 2004
LINKS
FORMULA
a(n) = 5^floor((n-1)/2).
a(1)=1, a(2)=1 and, for n > 2, a(n) = 5*a(n-2).
From Paul Barry, Feb 12 2004: (Start)
G.f.: x*(1+x)/(1-5*x^2);
a(n) = (1/(2*sqrt(5))*((1+sqrt(5))*(sqrt(5))^n - (1-sqrt(5))*(-sqrt(5))^n)).
Inverse binomial transform of A063727 (2^n*Fibonacci(n+1)). (End)
a(n+3) = a(n+2)*a(n+1)/a(n). - Reinhard Zumkeller, Mar 04 2011
MATHEMATICA
a[1] := 1; a[2] := 1; a[n_] := 5a[n - 2]; Table[a[n], {n, 30}] (* Alonso del Arte, Mar 04 2011 *)
PROG
(Magma) [5^Floor((n-1)/2): n in [1..40]]; // Vincenzo Librandi, Aug 16 2011
(PARI) a(n)=5^((n-1)\2) \\ Charles R Greathouse IV, Oct 03 2016
CROSSREFS
Sequence in context: A227076 A223186 A071340 * A162962 A056451 A170834
KEYWORD
nonn,easy
AUTHOR
John W. Layman, Sep 12 2002
STATUS
approved

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Last modified March 29 11:14 EDT 2024. Contains 371278 sequences. (Running on oeis4.)