OFFSET
0,1
COMMENTS
(sqrt(7)*csc(Pi/7)/2), (-sqrt(7)*csc(2*Pi/7)/2) and (-sqrt(7)*csc(4*Pi/7)/2) are the roots of the polynomial x^3 - 7*x - 7. - Corrected by Colin Barker, Aug 12 2016
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,7,7).
FORMULA
G.f.: (3 - 7*x^2)/(1 - 7*x^2 - 7*x^3). - Bruno Berselli, Aug 11 2016
a(n) = 7*a(n-2) + 7*a(n-3) with n>2, a(0)=3, a(1)=0, a(2)=14.
MATHEMATICA
RecurrenceTable[{a[0] == 3, a[1] == 0, a[2] == 14, a[n] == 7 a[n - 2] + 7 a[n - 3]}, a, {n, 0, 30}] (* Bruno Berselli, Aug 11 2016 *)
LinearRecurrence[{0, 7, 7}, {3, 0, 14}, 40] (* Harvey P. Dale, Jan 01 2022 *)
PROG
(PARI) Vec((3-7*x^2)/(1-7*x^2-7*x^3) + O(x^30)) \\ Colin Barker, Aug 12 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Kai Wang, Aug 11 2016
EXTENSIONS
Name and comment corrected by Colin Barker, Aug 12 2016
STATUS
approved