|
Search: id:A099471
|
|
|
| A099471 |
|
A sequence generated from the Quadrifoil (flat knot). |
|
+0
2
|
|
| 0, -2, -3, -1, 3, 5, 2, -4, -7, -3, 5, 9, 4, -6, -11, -5, 7, 13, 6, -8, -15, -7, 9, 17, 8, -10, -19, -9, 11, 21, 10, -12, -23, -11, 13, 25, 12, -14, -27, -13, 15, 29, 14, -16, -31, -15, 17, 33, 16, -18, -35, -17, 19, 37, 18, -20, -39, -19
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
a(3n), n = 1,2,3... = 2n + 1, unsigned. Odifreddi, p. 135 states: "Since the trefoil has polynomial x^2 - x + 1 and the quadrifoil (or flat knot) is the sum of two trefoils, its polynomial is (x^2 - x + 1) = x^4 - 2x^3 + 3x^2 - 2x + 1."
|
|
REFERENCES
|
Odifreddi, Piergiorgio; "The Mathematical Century; The 30 Greatest Problems of the Last 100 Years"; Princeton University Press, p. 135.
|
|
FORMULA
|
a(n) = M^n * [1 1 1 1], rightmost term; where M = the 4 X 4 companion matrix to the Quadrifoil polynomial x^4 - 2x^3 + 3x^2 - 2x + 1: [0 1 0 0 / 0 0 1 0 / 0 0 0 1 / -1 2 -3 2].
|
|
EXAMPLE
|
a(6) = 5 since M^6 * [1 1 1 1] = [ -3 -1 3 5].
|
|
CROSSREFS
|
Cf. A099470.
Sequence in context: A050375 A154722 A035517 this_sequence A121775 A127951 A162609
Adjacent sequences: A099468 A099469 A099470 this_sequence A099472 A099473 A099474
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 17 2004
|
|
|
Search completed in 0.002 seconds
|
