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

Author

Floor van Lamoen, Jan 19 2001

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A059503.

Programs

Mathematica

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

PARI

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

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