A122011 G.f. x^2*(1+x)/(1-12*x+15*x^2-2*x^3).

0, 1, 13, 141, 1499, 15899, 168585, 1787533, 18953419, 200965203, 2130856217, 22593703397, 239563527915, 2540118496459, 26933156445577, 285575226955869, 3027985613779691, 32106065273909411, 340424149534129305

Offset

1,3

Comments

Limit a(n+1)/a(n) = 10.6031 for n-> infinity.

References

"Linear Algebra, Examples and Applications" by Alain M. Robert, World Scientific, 2005, p. 58.

Links

Table of n, a(n) for n=1..19.

Index entries for linear recurrences with constant coefficients, signature (12, -15, 2).

Formula

a(n)= 12*a(n-1) -15*a(n-2) +2*a(n-3).

Mathematica

M = {{1, 1, 1}, {1, 2, 4}, {1, 3, 9}} v[1] = {1, 0, 0} v[n_] := v[n] = M.v[n - 1] a1 = Table[v[n][[3]], {n, 1, 50}]
Rest[CoefficientList[Series[x^2(1+x)/(1-12x+15x^2-2x^3), {x, 0, 30}], x]] (* or *) LinearRecurrence[{12, -15, 2}, {0, 1, 13}, 30] (* Harvey P. Dale, Oct 26 2013 *)

Crossrefs

Cf. A122009, A122010

Sequence in context: A263480 A210766 A045742 * A221103 A239250 A029483

Adjacent sequences: A122008 A122009 A122010 * A122012 A122013 A122014

Keyword

nonn,easy

Author

Roger L. Bagula and Gary W. Adamson, Sep 11 2006

Extensions

Definition replaced with generating function by the Assoc. Eds. of the OEIS, Mar 27 2010

Status

approved