login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A095003 a(n) = 9*a(n-1) - 9*a(n-2) + a(n-3). 2
1, 6, 45, 352, 2769, 21798, 171613, 1351104, 10637217, 83746630, 659335821, 5190939936, 40868183665, 321754529382, 2533168051389, 19943589881728, 157015551002433, 1236180818137734, 9732430994099437, 76623267134657760, 603253706083162641, 4749406381530643366 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
a(n)/a(n-1) tends to 7.87298... = 4 + sqrt(15) = C (having the property that C + 1/C = 8). Eigenvalues of M are C, 1/C, 1; being roots of x^3 - 9x^2 + 9x - 1.
LINKS
FORMULA
a(n+3) = 9*a(n+2) - 9*a(n+1) + a(n); given a(1) = 1, a(2) = 6, a(3) = 45.
Let M be the 3 X 3 matrix [1 1 1 / 1 2 3 / 1 3 6]. M^n * [1 0 0] = [A095002(n) a(n) A095004(n)].
EXAMPLE
a(4) = 352 since M^4 * [1 0 0] = [145, 352, 640].
MAPLE
a:= n-> (<<1|1|1>, <1|2|3>, <1|3|6>>^n)[1, 2]:
seq(a(n), n=1..23); # Alois P. Heinz, Jun 06 2021
MATHEMATICA
a[n_] := (MatrixPower[{{1, 1, 1}, {1, 2, 3}, {1, 3, 6}}, n].{{1}, {0}, {0}})[[2, 1]]; Table[ a[n], {n, 20}]; (* Robert G. Wilson v, May 29 2004 *)
LinearRecurrence[{9, -9, 1}, {1, 6, 45}, 30] (* Harvey P. Dale, Nov 12 2022 *)
CROSSREFS
Sequence in context: A024077 A097129 A048663 * A004988 A257633 A371779
KEYWORD
nonn
AUTHOR
Gary W. Adamson, May 27 2004
EXTENSIONS
Edited and extended by Robert G. Wilson v, May 29 2004
Definition corrected and edited by Georg Fischer, Jun 06 2021
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 20 23:53 EDT 2024. Contains 373535 sequences. (Running on oeis4.)