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A046978 Numerators of Taylor series for exp(x)*sin(x). 8
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. - 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 entries for 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). - Artur Jasinski, Oct 06 2008

a(n) = sign(cos(Pi*(n-2)/4)). - Wesley Ivan Hurt, Oct 02 2013

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}] (* Artur Jasinski, Oct 06 2008 *)

Table[Sign[Cos[Pi*(n-2)/4]], {n, 0, 100}] (* Wesley Ivan Hurt, Oct 10 2013 *)

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

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Last modified December 3 12:45 EST 2016. Contains 278734 sequences.