|
|
A099444
|
|
A Chebyshev transform of Fib(2n+2).
|
|
2
|
|
|
1, 3, 7, 15, 32, 69, 149, 321, 691, 1488, 3205, 6903, 14867, 32019, 68960, 148521, 319873, 688917, 1483735, 3195552, 6882329, 14822619, 31923791, 68754951, 148079008, 318920925, 686866813, 1479319737, 3186042539, 6861847920
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
The denominator is a parameterization of the Alexander polynomial for the knot 6_2 (Miller Institute knot). The g.f. is the image of the g.f. of Fib(2n+2) under the Chebyshev transform A(x)->(1/(1+x^2))A(x/(1+x^2)).
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (1+x^2)/(1-3x+3x^2-3x^3+x^4);
a(n) = sum{k=0..floor(n/2), binomial(n-k, k)(-1)^k*Fib(2(n-2k)+2)};
a(n) = sum{k=0..n, binomial((n+k)/2, k)(-1)^((n-k)/2)(1+(-1)^(n+k))Fib(2k+2)/2};
a(n) = sum{k=0..n, A099445(n-k)*binomial(1, k/2)(1+(-1)^k)/2}.
|
|
MATHEMATICA
|
LinearRecurrence[{3, -3, 3, -1}, {1, 3, 7, 15}, 30] (* Harvey P. Dale, Sep 30 2018 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|