A059505 Transform of A059502 applied to sequence 2,3,4,...

2, 5, 14, 40, 114, 323, 910, 2551, 7120, 19796, 54852, 151525, 417434, 1147145, 3145394, 8606848, 23507190, 64093031, 174474790, 474261691, 1287398452, 3490267820, 9451319304, 25565098825, 69080289074

Offset: 1

Author

Floor van Lamoen, Jan 19 2001

Keywords

• easy
• nonn

Comments

The second row of the array A059503.

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. A000667, A059216, A059219, A059502.

Programs

Mathematica

LinearRecurrence[{6,-11,6,-1},{2,5,14,40}, 50] (* or *) Rest[CoefficientList[Series[x*(2 - 7*x + 6*x^2 - x^3)/(1 - 3*x + x^2)^2, {x,0,50}], x]] (* G. C. Greubel, Sep 10 2017 *)

PARI

x='x+O('x^50); Vec(x*(2-7*x+6*x^2-x^3)/(1-3*x+x^2)^2) \\ G. C. Greubel, Sep 10 2017

Formula

G.f.: x*(2 - 7*x + 6*x^2 - x^3)/(1 - 3*x + x^2)^2.

From G. C. Greubel, Sep 10 2017: (Start)

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

a(n) = ((3 - n)*Fibonacci(2*n) + (5 + 3*n)*Fibonacci(2*n - 1))/5. (End)