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A135344
a(n) = 3*a(n-1) - a(n-3) + 3*a(n-4).
1
1, 1, 1, 1, 5, 17, 53, 157, 469, 1405, 4217, 12653, 37961, 113881, 341641, 1024921, 3074765, 9224297, 27672893, 83018677, 249056029, 747168085, 2241504257, 6724512773, 20173538321, 60520614961, 181561844881, 544685534641, 1634056603925, 4902169811777
OFFSET
0,5
FORMULA
3*a(n) - a(n+1) = hexaperiodic 2, 2, 2, -2, -2, -2 = 2*A130151.
From Richard Choulet, Jan 02 2008: (Start)
a(n) = (1/14)*3^n + (1/6)*(-1)^n + (16/21)*cos(Pi*n/3) + (8*sqrt(3)/21)*sin(Pi*n/3).
a(n) = (1/14)*3^n + (1/14)*[13; 11; 5; -13; -11; -5]. (End)
G.f.: ( -1+2*x+2*x^2+x^3 ) / ( (3*x-1)*(1+x)*(x^2-x+1) ). - Harvey P. Dale, Apr 15 2012
42*a(n) = 7*(-1)^n +8*A167380(n+3) +3^(n+1). - R. J. Mathar, Oct 03 2021
MATHEMATICA
LinearRecurrence[{3, 0, -1, 3}, {1, 1, 1, 1}, 40] (* Harvey P. Dale, Apr 15 2012 *)
CROSSREFS
Cf. A007395.
Sequence in context: A294781 A110318 A088210 * A222160 A027028 A176086
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Dec 06 2007
STATUS
approved