OFFSET
1,2
COMMENTS
Positive values of x (or y) satisfying x^2 - 16xy + y^2 + 14 = 0. - Colin Barker, Feb 11 2014
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..200
J.-C. Novelli, J.-Y. Thibon, Hopf Algebras of m-permutations,(m+1)-ary trees, and m-parking functions, arXiv preprint arXiv:1403.5962 [math.CO], 2014.
Index entries for linear recurrences with constant coefficients, signature (16,-1).
FORMULA
G.f.: x*(1-x) / ( 1-16*x+x^2 ). - R. J. Mathar, Oct 31 2011
a(n) = 16*a(n-1)-a(n-2). - Colin Barker, Feb 11 2014
a(n) = (1/18)*(9-sqrt(63))*(1+(8+sqrt(63))^(2*n-1))/(8+sqrt(63))^(n-1). [Bruno Berselli, Feb 25 2014]
a(n) = sqrt(2+(8-3*sqrt(7))^(1+2*n)+(8+3*sqrt(7))^(1+2*n))/(3*sqrt(2)). - Gerry Martens, Jun 06 2015
MAPLE
f:= gfun:-rectoproc({a(n)=16*a(n-1)-a(n-2), a(1)=1, a(2)=15}, a(n), remember):
map(f, [$1..30]); # Robert Israel, Jul 07 2015
MATHEMATICA
CoefficientList[Series[(1 - x)/(1 - 16 x + x^2), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 12 2014 *)
LinearRecurrence[{16, -1}, {1, 15}, 20] (* Harvey P. Dale, Sep 17 2019 *)
PROG
(Magma) I:=[1, 15]; [n le 2 select I[n] else 16*Self(n-1)-Self(n-2): n in [1..30]]; // Vincenzo Librandi, Feb 12 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Weisenhorn, Mar 01 2009
EXTENSIONS
New name (using the g.f. by R. J. Mathar) from Joerg Arndt, Jun 06 2015
STATUS
approved