|
Search: id:A143055
|
|
|
| A143055 |
|
The real part of complex sequence: a(n)=a(n-1)+(1+I)*a(n-1). |
|
+0
1
|
|
| 0, 1, 1, 2, 3, 4, 5, 4, -1, -16, -51, -124, -265, -520, -955, -1652, -2689, -4080, -5635, -6668, -5433, 1896, 22965, 72028, 174095, 370496, 725101, 1328452, 2292823, 3722904, 5631525
(list; graph; listen)
|
|
|
OFFSET
|
1,4
|
|
|
COMMENT
|
The ratio real absolute value approaches:1.744900645213449
|
|
FORMULA
|
a(n)=a(n-1)+(1+I)*a(n-1); a(n)_out=realpart(a(n)).
G.f.: x^2*(1-x-x^2)/(1-2x-x^2+2x^3+2x^4). a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -2*a(n-4). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 24 2008]
|
|
EXAMPLE
|
The imaginary part is:
0, 0, 0, 1, 2, 5, 10, 19, 34, 57, 90, 131, 170, 177, 82, -261, -1134, -3047,
-6870, -13997, -26502, -47167, -79102, -124373, -180510, -232855, -239270,
-101629, 384202, 1611025, 4288050
|
|
MATHEMATICA
|
Clear[a, n]; a[0] = 0; a[1] = 1; a[n_] := a[n] = a[n - 1] + (1 + I)*a[n - 2]; Table[Re[a[n]], {n, 0, 30}]
|
|
CROSSREFS
|
Sequence in context: A111615 A053627 A125746 this_sequence A017890 A134011 A035343
Adjacent sequences: A143052 A143053 A143054 this_sequence A143056 A143057 A143058
|
|
KEYWORD
|
uned,sign
|
|
AUTHOR
|
Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 13 2008
|
|
|
Search completed in 0.002 seconds
|
