|
Search: id:A121646
|
|
|
| A121646 |
|
Real part of (Fib(n-1) + Fib(n)*i)^2. |
|
+0
2
|
|
| -1, 0, -3, -5, -16, -39, -105, -272, -715, -1869, -4896, -12815, -33553, -87840, -229971, -602069, -1576240, -4126647, -10803705, -28284464, -74049691, -193864605, -507544128, -1328767775, -3478759201, -9107509824, -23843770275, -62423800997, -163427632720
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
Coresponding imaginary part = A079472(n); e.g. (3 + 5i)^2 = (-16 + 30i) where 30 = A079472(5). Consider a(n) and A079472(n) as legs of a Pythagorean triangle. Then hypotenuse = corresponding n-th term in the sequence (1, 2, 5, 13...; i.e. odd indexed Fibonacci terms.) a(n)/a(n-1) tends to Phi^2.
|
|
REFERENCES
|
Daniele Corradetti, La Metafisica del Numero, 2008
|
|
FORMULA
|
a(n) = Re:(F(n-1 + Fn*i)^2 a(n) = (F(n-1))^2 - (Fn)^2.
G.f.: (1-3x)/((1+x)(1-3x+x^2)); - Paul Barry (pbarry(AT)wit.ie), Oct 13 2006
|
|
EXAMPLE
|
a(5) = -16 since Re:(3 + 5i)^2 = (-16 + 30i).
a(5) = -16 = 3^2 - 5^2.
|
|
MAPLE
|
seq(-1*(fibonacci(i)*fibonacci(i+3)), i=-1..27); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 23 2007
|
|
MATHEMATICA
|
f[n_] := Re[(Fibonacci[n - 1] + I*Fibonacci[n])^2]; Array[f, 29] - Robert G. Wilson v, Aug 16 2006
|
|
CROSSREFS
|
Cf. A079472.
Sequence in context: A077551 A106588 A123785 this_sequence A099101 A038120 A105408
Adjacent sequences: A121643 A121644 A121645 this_sequence A121647 A121648 A121649
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 13 2006
|
|
EXTENSIONS
|
More terms from Robert G. Wilson v, Aug 16 2006
|
|
|
Search completed in 0.002 seconds
|
