A059506 Transform of A059502 applied to sequence 3,4,5,...

3, 7, 19, 53, 148, 412, 1143, 3161, 8717, 23977, 65798, 180182, 492459, 1343563, 3659623, 9953117, 27031768, 73320496, 198632607, 537507677, 1452978593, 3923762257, 10586222474, 28536313898, 76859031123

Offset

1,1

Comments

The third 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).

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*(1-x)*(2*x^2-8*x+3)/(x^2-3*x+1)^2. (End)

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

Mathematica

LinearRecurrence[{6, -11, 6, -1}, {3, 7, 19, 53}, 30] (* Harvey P. Dale, Jul 30 2015 *)
Rest[CoefficientList[Series[x*(1 - x)*(2*x^2 - 8*x + 3)/(x^2 - 3*x + 1)^2, {x, 0, 50}], x]] (* G. C. Greubel, Sep 10 2017 *)

Prog

(PARI) Vec(x*(1-x)*(2*x^2-8*x+3)/(x^2-3*x+1)^2 + O(x^30)) \\ Michel Marcus, Sep 09 2017

Crossrefs

Cf. A000667, A059216, A059219, A059502.

Sequence in context: A222324 A007180 A090378 * A007575 A026299 A183117

Adjacent sequences: A059503 A059504 A059505 * A059507 A059508 A059509

Keyword

easy,nonn

Author

Floor van Lamoen, Jan 19 2001

Status

approved