|
|
A083696
|
|
a(n) = Sum_{r=0..2^(n-1)} (5^r/(2r)!)*Product_{k=0..2r-1} (2^n - k).
|
|
2
|
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Similar to A081459: a(n) is the numerator of the same mapping f(r) = (1/2)*(r + 5/r) but with initial value r=1.
|
|
LINKS
|
|
|
FORMULA
|
a(n)/A083697(n) converges to sqrt(5).
a(n) = a(n-1)^2 + 5*A083697(n-1)^2.
|
|
MATHEMATICA
|
Table[Sum[Product[2^n - k, {k, 0, 2*r - 1}]5^r/(2*r)!, {r, 0, 2^(n - 1)}], {n, 0, 8}]
|
|
PROG
|
(Sage) [2^(2^n -1)*lucas_number2(2^n, 1, -1) for n in (0..8)] # G. C. Greubel, Jan 14 2022
(Magma) [2^(2^n -1)*Lucas(2^n): n in [0..8]]; // G. C. Greubel, Jan 14 2022
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Mario Catalani (mario.catalani(AT)unito.it), May 22 2003
|
|
STATUS
|
approved
|
|
|
|