A140230 -id:A140230 - cp's OEIS frontend

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

Paul Curtz, Apr 22 2011

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).

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

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

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

More terms from Jinyuan Wang, Feb 26 2020

A316386 Binomial transform of [0, 1, 2, -3, -4, 5, 6, -7, -8, ...].

Original entry on oeis.org

0, 1, 4, 6, 0, -20, -48, -56, 0, 144, 320, 352, 0, -832, -1792, -1920, 0, 4352, 9216, 9728, 0, -21504, -45056, -47104, 0, 102400, 212992, 221184, 0, -475136, -983040, -1015808, 0, 2162688, 4456448, 4587520, 0, -9699328, -19922944, -20447232, 0, 42991616

Offset: 0

Paul Curtz, Jul 01 2018

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-8,8,-4).

Cf. A009545, A140230.

seq(coeff(series(x*(1-2*x^2)/(1-2*x+2*x^2)^2, x,n+1),x,n),n=0..45); # Muniru A Asiru, Jul 01 2018

CoefficientList[Series[x (1 - 2 x^2)/(1 - 2 x + 2 x^2)^2, {x, 0, 41}], x] (* Michael De Vlieger, Jul 01 2018 *)
LinearRecurrence[{4, -8, 8, -4}, {0, 1, 4, 6}, 42] (* Robert G. Wilson v, Jul 15 2018 *)

concat(0, Vec(x*(1 - 2*x^2) / (1 - 2*x + 2*x^2)^2 + O(x^40))) \\ Colin Barker, Jul 01 2018

a(n) = n * A009545(n).
a(n+1) = a(n) + A140230(n).
From Colin Barker, Jul 01 2018: (Start)
G.f.: x*(1 - 2*x^2) / (1 - 2*x + 2*x^2)^2.
a(n) = 4*a(n-1) - 8*a(n-2) + 8*a(n-3) - 4*a(n-4) for n>3.
a(n) = i*(((1-i)^n - (1+i)^n)*n) / 2 where i=sqrt(-1).
(End)

More terms from Colin Barker, Jul 01 2018

cp's OEIS Frontend

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

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