|
|
A020732
|
|
Pisot sequence T(4,7).
|
|
1
|
|
|
4, 7, 12, 20, 33, 54, 88, 143, 232, 376, 609, 986, 1596, 2583, 4180, 6764, 10945, 17710, 28656, 46367, 75024, 121392, 196417, 317810, 514228, 832039, 1346268, 2178308, 3524577, 5702886, 9227464, 14930351, 24157816, 39088168, 63245985, 102334154, 165580140
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Fibonacci(n+5) - 1.
a(n) = 2*a(n-1) - a(n-3).
a(n) = (-1+(2^(-1-n)*((1-sqrt(5))^n*(-11+5*sqrt(5))+(1+sqrt(5))^n*(11+5*sqrt(5))))/sqrt(5)).
G.f.: (4-x-2*x^2) / ((1-x)*(1-x-x^2)).
(End)
|
|
MATHEMATICA
|
|
|
PROG
|
(PARI) Vec((4-x-2*x^2)/((1-x)*(1-x-x^2)) + O(x^50)) \\ Colin Barker, Mar 22 2016
|
|
CROSSREFS
|
Subsequence of A000071. See A008776 for definitions of Pisot sequences.
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|