A122010 G.f. x^2*(1-5*x)/(1-12*x+15*x^2-2*x^3).

0, 1, 7, 69, 725, 7679, 81411, 863197, 9152557, 97045551, 1028984651, 10910437661, 115684573269, 1226616283615, 13005947679667, 137903497048317, 1462205981952029, 15503931223058927, 164389891941523323

Offset

1,3

Comments

Limit a(n+1)/a(n) = 10.6031 as 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][[2]], {n, 1, 50}]
LinearRecurrence[{12, -15, 2}, {0, 1, 7}, 20] (* Harvey P. Dale, Mar 11 2022 *)

Crossrefs

Cf. A122009, A122011

Sequence in context: A133697 A224758 A219330 * A180911 A084774 A025757

Adjacent sequences: A122007 A122008 A122009 * A122011 A122012 A122013

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