OFFSET
0,2
COMMENTS
a(n)/a(n-1) tends to 9 + 4*sqrt(2) = 14.65685424... - Klaus Brockhaus, Sep 25 2009
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (18,-49).
FORMULA
G.f.: (1-9x)/(1-18x+49x^2);
e.g.f.: exp(9x)*cosh(4*sqrt(2)x);
a(n) = Sum_{k=0..n} 8^k*binomial(2n,2k) = Sum_{k=0..n} 8^k*A086645(n,k);
a(n) = 7^n*T(n,9/7) where T is the Chebyshev polynomial of the first kind;
a(n) = (1+sqrt(8))^(2n)/2 + (1-sqrt(8))^(2n)/2.
a(n) = ((9-4*sqrt(2))^n + (9+4*sqrt(2))^n)/2. - Klaus Brockhaus, Sep 25 2009
MATHEMATICA
LinearRecurrence[{18, -49}, {1, 9}, 20] (* Harvey P. Dale, Sep 30 2016 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Philippe Deléham, Sep 08 2009
STATUS
approved