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

Author

Floor van Lamoen, Jan 19 2001

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A000667, A059216, A059219, A059502.

Programs

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 *)

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

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