A046980 Numerators of Taylor series for exp(x)*cos(x).

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign
• frac
• easy
• nice

Comments

Lehmer sequence U_n for R=2 Q=1. [Artur Jasinski, Oct 06 2008]

Examples

			1 + 1*x - (1/3)*x^3 - (1/6)*x^4 - (1/30)*x^5 + (1/630)*x^7 + (1/2520)*x^8 + (1/22680)*x^9 - ...
		

References

• G. W. Caunt, Infinitesimal Calculus, Oxford Univ. Press, 1914, p. 477.

Links

• Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, -1).

Crossrefs

Cf. A046981.

Programs

Maple

A046980 := n -> `if`(n mod 4 = 2, 0, (-1)^floor((n+1)/4)):
seq(A046980(n), n=0..92); # Peter Luschny, Jun 16 2017

Mathematica

b = -((1 + I)/Sqrt[2]) + Sqrt[2]; c = (1 + I)/Sqrt[2]; Table[ Round[(b^n - c^n)/(b - c)], {n, 2, 200}] (* Artur Jasinski, Oct 06 2008 *)
LinearRecurrence[{0, 0, 0, -1}, {1, 1, 0, -1}, 100] (* Jean-François Alcover, Apr 01 2016 *)
PadRight[{},120,{1,1,0,-1,-1,-1,0,1}] (* Harvey P. Dale, Nov 02 2024 *)

Formula

G.f.: (1+x-x^3)/(1+x^4).

a(n) = (b^(n+1) - c^(n+1))/(b - c) where b = sqrt(2)-((1 + I)/sqrt(2)), c = (1 + I)/sqrt(2). [Artur Jasinski, Oct 06 2008]