A080041 a(n) = floor((1+sqrt(3))^n).

1, 2, 7, 20, 55, 152, 415, 1136, 3103, 8480, 23167, 63296, 172927, 472448, 1290751, 3526400, 9634303, 26321408, 71911423, 196465664, 536754175, 1466439680, 4006387711, 10945654784, 29904084991, 81699479552, 223207129087

Offset

0,2

Links

Table of n, a(n) for n=0..26.

Index entries for linear recurrences with constant coefficients, signature (2,3,-2,-2).

Formula

a(n) = A080040(n) - (1+(-1)^n)/2.

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

Mathematica

CoefficientList[Series[(1+2t^3)/(1-2t-3t^2+2t^3+2t^4), {t, 0, 30}], t]
Floor[(1+Sqrt[3])^Range[0, 30]] (* Harvey P. Dale, Sep 14 2012 *)

Crossrefs

Cf. A080040.

Sequence in context: A035508 A018033 A000149 * A049681 A027120 A094982

Adjacent sequences: A080038 A080039 A080040 * A080042 A080043 A080044

Keyword

easy,nonn

Author

Mario Catalani (mario.catalani(AT)unito.it), Jan 21 2003

Status

approved