A116561 Sequentially switched Markov of six determinant one matrices.

0, 1, 4, 4, 18, 7, 7, 18, 79, 79, 359, 140, 140, 359, 1576, 1576, 7162, 2793, 2793, 7162, 31441, 31441, 142881, 55720, 55720, 142881, 627244, 627244, 2850458, 1111607, 1111607, 2850458, 12513439, 12513439, 56866279, 22176420, 22176420

Offset

0,3

Comments

The recurrence means that these are 6 interlaced sequences (2 of them equal) of the type b(n) = 20*b(n-1) - b(n-2). The generating function shows a(n) can be written as a sum of 10 terms of A075843. - R. J. Mathar, Nov 26 2008

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,20,0,0,0,0,0,-1).

Formula

From R. J. Mathar, Nov 26 2008: (Start)

a(n) = 20*a(n-6) -a(n-12).

G.f: x*(1 +4*x +4*x^2 +18*x^3 +7*x^4 +7*x^5 -2*x^6 -x^7 -x^8 -x^9) / (1-20*x^6+x^12). (End)

Mathematica

LinearRecurrence[{0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, -1}, {0, 1, 4, 4, 18, 7, 7, 18, 79, 79, 359, 140}, 37] (* Ray Chandler, Aug 11 2015 *)
CoefficientList[Series[x *(1 + 4*x + 4*x^2 + 18*x^3 + 7*x^4 + 7*x^5 - 2*x^6 - x^7 - x^8 - x^9)/(1 - 20*x^6 + x^12), {x, 0, 50}], x] (* G. C. Greubel, Sep 20 2017 *)

Prog

(PARI) x=+O('x^50); Vec(x*(1 +4*x +4*x^2 +18*x^3 +7*x^4 +7*x^5 -2*x^6 -x^7 -x^8 -x^9) / (1-20*x^6+x^12)) \\ G. C. Greubel, Sep 20 2017

Crossrefs

Sequence in context: A193961 A368197 A205110 * A086448 A128090 A119948

Adjacent sequences: A116558 A116559 A116560 * A116562 A116563 A116564

Keyword

nonn,obsc

Author

Roger L. Bagula, Mar 17 2006

Status

approved