A132353 - OEIS

A132353

a(n) = 3*a(n-1) - a(n-3) + 3*a(n-4), starting with 1, 2, 6, 20.

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

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OFFSET

0,2

COMMENTS

A132868(n) - a(n) = A128834(n) (discovered in 1995).

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,0,-1,3).

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

Adjacent sequences: A132350 A132351 A132352 * A132354 A132355 A132356

KEYWORD

nonn

AUTHOR

Paul Curtz, Nov 24 2007

EXTENSIONS

More terms from R. J. Mathar, Apr 04 2008

STATUS

approved