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A116561
Expansion of 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).
1
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
Previous name was: Sequentially switched Markov of six determinant one matrices.
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
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
KEYWORD
nonn,easy,less
AUTHOR
Roger L. Bagula, Mar 17 2006
EXTENSIONS
Better name using given g.f. from Joerg Arndt, Oct 26 2024
STATUS
approved