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A135343
a(n) = 3*a(n-1) + 4*a(n-2) - a(n-3) + 3*a(n-4) + 4*a(n-5).
3
1, 3, 12, 51, 205, 820, 3277, 13107, 52428, 209715, 838861, 3355444, 13421773, 53687091, 214748364, 858993459, 3435973837, 13743895348, 54975581389, 219902325555, 879609302220, 3518437208883, 14073748835533, 56294995342132, 225179981368525, 900719925474099
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?
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
Sequence in context: A009024 A265083 A043291 * A083314 A155179 A228770
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