A018186 a(n+2) = 3*a(n) - a(n-2) with a(0) = 1, a(1) = 3, a(2) = 6.

1, 3, 6, 9, 19, 30, 63, 99, 208, 327, 687, 1080, 2269, 3567, 7494, 11781, 24751, 38910, 81747, 128511, 269992, 424443, 891723, 1401840, 2945161, 4629963, 9727206, 15291729, 32126779, 50505150, 106107543, 166807179, 350449408, 550926687, 1157455767, 1819587240

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

J. L. Simons, Conditional recurring sequences, Doctor's Thesis, Delft University of Technology, Delft, 1976 (MR 54 #7361).

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

Formula

G.f.: (1+3*x+3*x^2)/(1-3*x^2-x^4).

Mathematica

CoefficientList[Series[(1 + 3 x + 3 x^2) / (1 - 3 x^2 - x^4), {x, 0, 40}], x] (* Vincenzo Librandi, Sep 10 2013 *)
LinearRecurrence[{0, 3, 0, 1}, {1, 3, 6, 9}, 40] (* Harvey P. Dale, Jul 19 2015 *)

Prog

(PARI) lista(nn) = {x = xx + xx*O(xx^nn); expr = (1 + 3*x + 3*x^2)/(1 - 3*x^2 - x^4); for (i = 0, nn, print1(polcoeff(expr, i, xx), ", "); ); } \\ Michel Marcus, Sep 09 2013
(PARI) Vec( (1+3*x+3*x^2)/(1-3*x^2-x^4)+O(x^66) ) \\ Joerg Arndt, Sep 09 2013
(Magma) m:=40; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1+3*x+3*x^2)/(1-3*x^2-x^4)); // Vincenzo Librandi, Sep 10 2013

Crossrefs

Sequence in context: A059006 A342596 A363124 * A223504 A322949 A285215

Adjacent sequences: A018183 A018184 A018185 * A018187 A018188 A018189

Keyword

nonn,easy

Author

H. J. J. te Riele (Herman.te.Riele(AT)cwi.nl)

Extensions

More terms from Michel Marcus, Sep 09 2013

Status

approved