A059509 Main diagonal of the array A059503.

1, 5, 19, 66, 216, 679, 2075, 6211, 18299, 53244, 153366, 438095, 1242709, 3504161, 9830371, 27454614, 76375860, 211732471, 585157679, 1612689439, 4433421131, 12160156560, 33284285874, 90931830431, 247991356201, 675243561149, 1835863145395, 4984516006506, 13516071450384

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for sequences related to boustrophedon transform

Index entries for linear recurrences with constant coefficients, signature (6,-11,6,-1).

Formula

From Colin Barker, Nov 30 2012: (Start)

a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) - a(n-4).

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

a(n) = ((3 - n)*Fibonacci(2*n) - (5 - 8*n)*Fibonacci(2*n - 1))/5. - G. C. Greubel, Sep 10 2017

E.g.f.: 1 + exp(3*x/2)*(5*(7*x - 5)*cosh(sqrt(5)*x/2) + sqrt(5)*(5*x + 11)*sinh(sqrt(5)*x/2))/25. - Stefano Spezia, Apr 11 2025

Mathematica

Rest[CoefficientList[Series[x*(x^3 - x + 1)/(x^2 - 3*x + 1)^2, {x, 0, 50}], x]] (* G. C. Greubel, Sep 10 2017 *)
(* Alternative: *)
Table[((3 - n)*Fibonacci[2*n] - (5 - 8*n)*Fibonacci[2*n - 1])/5, {n, 1, 50}] (* G. C. Greubel, Sep 10 2017 *)

Prog

(PARI) Vec(x*(x^3-x+1)/(x^2-3*x+1)^2 + O(x^40)) \\ Michel Marcus, Sep 09 2017

Crossrefs

Cf. A059503.

Sequence in context: A099448 A239618 A124806 * A137745 A382989 A005021

Adjacent sequences: A059506 A059507 A059508 * A059510 A059511 A059512

Keyword

easy,nonn,changed

Author

Floor van Lamoen, Jan 19 2001

Status

approved