OFFSET
0,2
COMMENTS
See A129339 comments. Third sequence after b(n) = 3*b(n-1) - 3*b(n-2) + 2*b(n-3) and c(n) = 3*c(n-1) - c(n-3) + 3*c(n-4). The first is for every sequence identical to its third differences. What characterizes the two others?
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3, 4, -1, 3, 4).
FORMULA
a(n+1) - 4*a(n) = hexaperiodic -1, 0, 3, 1, 0, -3.
a(n) = (1/15)*( 3*4^(n+1) - 2*(-1)^n + 5*cos(Pi*n/3) - 5*sqrt(3)*cos(Pi*n/3) ). - Richard Choulet, Jan 04 2008
G.f.: (1-x+4*x^3) / ((1+x)*(1-4*x)*(1-x+x^2)). - Colin Barker, Oct 11 2016
MATHEMATICA
LinearRecurrence[{3, 4, -1, 3, 4}, {1, 3, 12, 51, 205}, 30] (* Harvey P. Dale, Jun 03 2013 *)
PROG
(PARI) Vec((1-x+4*x^3)/((1+x)*(1-4*x)*(1-x+x^2)) + O(x^30)) \\ Colin Barker, Oct 11 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Dec 05 2007
EXTENSIONS
More terms from Harvey P. Dale, Jun 03 2013
Removed incorrect formula, Joerg Arndt, Oct 11 2016
STATUS
approved