A189442 a(n) = A140230(n) / A016116(n-1).

1, 3, 1, -3, -5, -7, -1, 7, 9, 11, 1, -11, -13, -15, -1, 15, 17, 19, 1, -19, -21, -23, -1, 23, 25, 27, 1, -27, -29, -31, -1, 31, 33, 35, 1, -35, -37, -39, -1, 39, 41, 43, 1, -43, -45, -47, -1, 47, 49, 51, 1, -51, -53, -55, -1, 55, 57, 59, 1, -59, -61, -63, -1, 63

Offset

1,2

Comments

If grouped into blocks of four,

1, 3, 1, -3,

-5, -7, -1, 7,

9, 11, 1, -11,

-13, -15, -1, 15

17, 19, 1, -19.

we see that a(4n+1) + a(4n+2) + a(4n+3) + a(4n+4) = (-1)^n*(2+4*n).

Links

Table of n, a(n) for n=1..64.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,-2,0,0,0,-1).

Formula

a(n) = -2*a(n-4) - a(n-8). a(n) + a(n-4) = period length 8: repeat -4, -4, 0, 4, 4, 4, 0 -4.

G.f. x*(x-1)*(x^4-2*x-1)*(1+x)^2 / (x^4+1)^2. - R. J. Mathar, Jun 02 2011

a(n) = (-1)^floor(n/4)*(1+3*n+(n-1)*(-1)^n-4*cos(n*Pi/2)+2*(n-1)*sin(n*Pi/2) )/4. - Wesley Ivan Hurt, May 08 2021

Prog

(PARI) Vec(x*(x-1)*(x^4-2*x-1)*(1+x)^2 / (x^4+1)^2+O(x^99)) \\ Charles R Greathouse IV, Jun 08 2011

Crossrefs

Sequence in context: A321906 A321904 A321903 * A320562 A320561 A321902

Adjacent sequences: A189439 A189440 A189441 * A189443 A189444 A189445

Keyword

sign,easy

Author

Paul Curtz, Apr 22 2011

Extensions

More terms from Jinyuan Wang, Feb 26 2020

Status

approved