|
| |
|
|
A046978
|
|
Numerators of Taylor series for exp(x)*sin(x).
|
|
6
|
|
|
|
0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,1
|
|
|
COMMENTS
|
Period 8: repeat [0, 1, 1, 1, 0, -1, -1, -1].
Lehmer sequence U_n for R=2 Q=1 [From Artur Jasinski, Oct 06 2008]
4*a(n+6) = period 8: repeat -4,-4,0,4,4,4,0,-4 = A189442(n+1) + A189442(n+5). - Paul Curtz, Jun 03 2011
|
|
|
REFERENCES
|
G. W. Caunt, Infinitesimal Calculus, Oxford Univ. Press, 1914, p. 477.
|
|
|
LINKS
|
Table of n, a(n) for n=0..104.
Index to sequences with linear recurrences with constant coefficients, signature (0,0,0,-1).
|
|
|
FORMULA
|
Euler transform of length 8 sequence [ 1, 0, -1, -1, 0, 0, 0, 1]. - Michael Somos, Jul 16 2006
G.f.: x * (1 + x + x^2) / (1 + x^4) = x * (1 - x^3) * (1 - x^4) / ((1 - x) * (1 - x^8)). a(-n) = a(n + 4) = -a(n). - Michael Somos, Jul 16 2006
a(n)=round((b^n - c^n)/(b - c)) where b = sqrt(2)-((1+i)/sqrt(2)), c = (1+i)/sqrt(2) [From Artur Jasinski, Oct 06 2008]
|
|
|
EXAMPLE
|
x + x^2 + x^3 - x^5 - x^6 - x^7 + x^9 + x^10 + x^11 - x^13 - x^14 - ...
1*x +1*x^2 +1/3*x^3 -1/30*x^5 -1/90*x^6 -1/630*x^7 +1/22680*x^9 +1/113400*x^10+...
|
|
|
MAPLE
|
A046978 := n -> `if`(n mod 4 = 0, 0, (-1)^iquo(n, 4)): # Peter Luschny, Aug 21 2011
|
|
|
MATHEMATICA
|
a = -((1 + I)/Sqrt[2]) + Sqrt[2]; b = (1 + I)/Sqrt[2]; Table[ Round[(a^n - b^n)/(a - b)], {n, 0, 200}] [From Artur Jasinski, Oct 06 2008]
|
|
|
PROG
|
(PARI) a(n)=(n%4 > 0) * (-1)^(n\4) /* Michael Somos, Jul 16 2006 */
|
|
|
CROSSREFS
|
Cf. A046979.
Sequence in context: A098725 A166486 * A075553 A131729 A144609 A115517
Adjacent sequences: A046975 A046976 A046977 * A046979 A046980 A046981
|
|
|
KEYWORD
|
sign,frac,easy
|
|
|
AUTHOR
|
N. J. A. Sloane.
|
|
|
STATUS
|
approved
|
| |
|
|
