A122009 G.f. x*(1-11*x+6*x^2)/(1-12*x+15*x^2-2*x^3).

1, 1, 3, 23, 233, 2457, 26035, 276031, 2926761, 31032737, 329043491, 3488884359, 36993025417, 392241126601, 4158975906675, 44098080031919, 467576804036105, 4957768399767825, 52567764896736163, 557381806372388791

Offset

1,3

References

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

Links

Table of n, a(n) for n=1..20.

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

Formula

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

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][[1]], {n, 1, 50}]
LinearRecurrence[{12, -15, 2}, {1, 1, 3}, 30] (* Harvey P. Dale, Feb 23 2025 *)

Crossrefs

Cf. A122011, A122010

Sequence in context: A068146 A162591 A278745 * A360987 A151433 A199750

Adjacent sequences: A122006 A122007 A122008 * A122010 A122011 A122012

Keyword

nonn,easy,changed

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