A135343 a(n) = 3*a(n-1) + 4*a(n-2) - a(n-3) + 3*a(n-4) + 4*a(n-5).

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?

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

Cf. A129339, A135345.

Sequence in context: A009024 A265083 A043291 * A083314 A155179 A228770

Adjacent sequences: A135340 A135341 A135342 * A135344 A135345 A135346

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