OFFSET
0,3
COMMENTS
LINKS
Daniel Poveda Parrilla, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (13,13,-1).
FORMULA
a(n) = 14*a(n-1) - a(n-2) - 4*(-1)^n for n>1, a(0)=0, a(1)=1.
From Colin Barker, Sep 23 2016: (Start)
G.f.: x*(1 - 3*x) / ((1 + x)*(1 - 14*x + x^2)).
a(n) = 13*a(n-1) + 13*a(n-2) - a(n-3) for n>2.
a(n) = ( -6*(-1)^n + (3+sqrt(3))*(7-4*sqrt(3))^n - (-3+sqrt(3))*(7+4*sqrt(3))^n )/24. (End)
MATHEMATICA
RecurrenceTable[{a[n] == 14 a[n - 1] - a[n - 2] - 4 (-1)^n, a[0] == 0, a[1] == 1}, a, {n, 19}] (* Michael De Vlieger, Sep 23 2016 *)
PROG
(PARI) concat(0, Vec(x*(1-3*x)/((1+x)*(1-14*x+x^2)) + O(x^30))) \\ Colin Barker, Sep 23 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Daniel Poveda Parrilla, Sep 22 2016
STATUS
approved