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A132353
a(n) = 3*a(n-1) - a(n-3) + 3*a(n-4), starting with 1, 2, 6, 20.
2
1, 2, 6, 20, 61, 183, 547, 1640, 4920, 14762, 44287, 132861, 398581, 1195742, 3587226, 10761680, 32285041, 96855123, 290565367, 871696100, 2615088300, 7845264902, 23535794707, 70607384121, 211822152361, 635466457082
OFFSET
0,2
COMMENTS
A132868(n) - a(n) = A128834(n) (discovered in 1995).
FORMULA
Also a(n) - 3^(n+1) = hexaperiodic 1, -1, -3, -1, 1, 3; cf. A132951.
From R. J. Mathar, Apr 04 2008: (Start)
O.g.f.: (1-x+3*x^3)/((1-3*x)*(1+x)*(x^2-x+1)).
a(n) = -(-1)^n/12 + 3^(n+1)/4 + A057079(n+2)/3. (End)
MATHEMATICA
LinearRecurrence[{3, 0, -1, 3}, {1, 2, 6, 20}, 50] (* G. C. Greubel, Jan 15 2018 *)
PROG
(PARI) x='x+O('x^30); Vec((1-x+3*x^3)/((1-3*x)*(1+x)*(x^2-x+1))) \\ G. C. Greubel, Jan 15 2018
(Magma) I:=[1, 2, 6, 20]; [n le 4 select I[n] else 3*Self(n-1) - Self(n-3) + 3*Self(n-4): n in [1..30]]; // G. C. Greubel, Jan 15 2018
CROSSREFS
Cf. A129339.
Sequence in context: A136883 A289173 A057766 * A263900 A260696 A052958
KEYWORD
nonn
AUTHOR
Paul Curtz, Nov 24 2007
EXTENSIONS
More terms from R. J. Mathar, Apr 04 2008
STATUS
approved