|
Search: id:A109532
|
|
|
| A109532 |
|
a(n)= +a(n-3) +2*a(n-6) +a(n-9). |
|
+0
2
|
|
| 1, 1, 1, 1, 3, 1, 3, 6, 3, 6, 13, 6, 13, 28, 13, 28, 60, 28, 60, 129, 60, 129, 277, 129, 277, 595, 277, 595, 1278, 595, 1278, 2745, 1278, 2745, 5896, 2745, 5896, 12664, 5896, 12664, 27201, 12664, 27201, 58425, 27201, 58425, 125491, 58425, 125491, 269542
(list; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
COMMENT
|
The recurrence shows that these are actually three interleaved sequences with
the same recurrence (and the same characteristic polynomial).
|
|
FORMULA
|
G.f.: (1+x+x^2+2*x^4+x^7)/(1-x^3-2*x^6-x^9).
|
|
MATHEMATICA
|
M1 = {{0, 1, 0}, {0, 0, 1}, {1, 1, 0}}; M2 = {{0, 1, 1}, {1, 0, 0}, {0, 1, 0}}; M3 = {{0, 1, 0}, {1, 0, 1}, {1, 0, 0}}; M[n_] = If[Mod[n, 3] == 1, M3, If[Mod[n, 3] == 2, M2, M1]]; v[0] = {0, 1, 1}; v[n_] := v[n] = M[n].v[n - 1] a = Table[v[n][[2]], {n, 0, 100}]
|
|
CROSSREFS
|
Cf. A000931, A109531, A109533.
Sequence in context: A107726 A114159 A033789 this_sequence A137338 A058659 A053642
Adjacent sequences: A109529 A109530 A109531 this_sequence A109533 A109534 A109535
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 18 2005
|
|
EXTENSIONS
|
Definition replaced by recurrence by the Associate Editors of the OEIS, Sep 28 2009
|
|
|
Search completed in 0.002 seconds
|
