OFFSET
0,2
COMMENTS
The general form of the g.f. for (A^(2*n+1)+B^(2*n+1))/(A+B) is (1-A*B*x)/((1-A^2*x)(1-B^2*x)).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..260
Index entries for linear recurrences with constant coefficients, signature (6817,-1679616).
FORMULA
G.f.: (1 - 16*81*x)/((1 - 16^2*x)*(1 - 81^2*x)).
a(n) = (16^2+81^2)*a(n-1) - 16^2*81^2*a(n-2).
EXAMPLE
a(0) = (16^1 + 81^1)/97 = 97/97 = 1.
a(1) = (16^3 + 81^3)/97 = 535537/97 = 5521.
MAPLE
seq(coeff(series((1-16*81*x)/((1-16^2*x)*(1-81^2*x)), x, n+1), x, n), n = 0 .. 10); # Muniru A Asiru, Oct 21 2018
MATHEMATICA
f[n_]:=Module[{c=2n+1}, (16^c+81^c)/97]; Array[f, 20, 0] (* Harvey P. Dale, Oct 02 2012 *)
PROG
(PARI) a(n)=(16^(2*n+1)+81^(2*n+1))/97
(Magma) [(2^(8*n+4) + 3^(8*n+4))/97: n in [0..20]]; // G. C. Greubel, Oct 20 2018
(GAP) List([0..10], n->(16^(2*n+1)+81^(2*n+1))/97); # Muniru A Asiru, Oct 21 2018
(Python) for n in range(0, 10): print(int((16**(2*n+1)+81**(2*n+1))/97), end=', ') # Stefano Spezia, Oct 21 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jaume Oliver Lafont, Sep 19 2009
EXTENSIONS
Definition replaced with formula by R. J. Mathar, Sep 21 2009
STATUS
approved