OFFSET
0,2
LINKS
Fumio Hazama, Spectra of graphs attached to the space of melodies, Discr. Math., 311 (2011), 2368-2383. See Table 2.1.
Index entries for linear recurrences with constant coefficients, signature (2,-1,0,1).
FORMULA
M = {{0, 0, 0, 1}, {1, 1, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 1}} v[n]=v[n-1].M a(n) = v[n][[1]].
a(n) = (1/2)*[Lucas(n+1) + 2*cos((n+4)*Pi/3)].
a(0)=0, a(1)=2, a(2)=3, a(3)=4, a(n) = 2*a(n-1)-a(n-2)+a(n-4). [Harvey P. Dale, Aug 19 2011]
MATHEMATICA
M = {{0, 0, 0, 1}, {1, 1, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 1}} v[1] = {0, 1, 1, 2}; v[n_] := v[n] = M.v[n - 1]; digits = 50; a = Table[v[n][[1]], {n, 1, digits}]
CoefficientList[Series[(x^2-2x)/(x^4-x^2+2x-1), {x, 0, 40}], x] (* or *) LinearRecurrence[{2, -1, 0, 1}, {0, 2, 3, 4}, 41] (* Harvey P. Dale, Aug 19 2011 *)
PROG
(PARI) Vec((x^2-2*x)/(x^4-x^2+2*x-1)+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, May 30 2005
STATUS
approved