A134874 Expansion of 1/(1 - 137 x - 133 x^4).

1, 137, 18769, 2571353, 352275494, 48261760899, 6611863739440, 905825674293229, 124098164230813075, 17001454918435590842, 2329200203203553290874, 319100548313701481849195

Offset

1,2

Comments

From characteristic polynomial of the matrix: {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {133, 0, 0, 137}}.

Polynomial base is Pisot and the large positiuve root is near 1/alpha: 137.00005172368373...

Links

Table of n, a(n) for n=1..12.

Index entries for linear recurrences with constant coefficients, signature (137, 0, 0, 133).

Formula

a(n) =Expansion(1/(1 - 137 x - 133 x^4))

Mathematica

mc = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {133, 0, 0, 137}}; f[x_] = CharacteristicPolynomial[mc, x]; g[x_] = Expand[x^4*f[1/x]]; Table[ SeriesCoefficient[Series[1/g[x], {x, 0, 30}], n], {n, 0, 30}]

Crossrefs

Sequence in context: A357131 A103878 A068154 * A064104 A300407 A122703

Adjacent sequences: A134871 A134872 A134873 * A134875 A134876 A134877

Keyword

nonn

Author

Roger L. Bagula, Jan 29 2008

Status

approved