A201837 G.f.: real part of 1/(1 - i*x - i*x^2) where i=sqrt(-1).

1, 0, -1, -2, 0, 4, 5, -2, -13, -12, 12, 40, 25, -52, -117, -38, 196, 324, -3, -678, -841, 360, 2200, 2000, -2079, -6760, -4121, 8918, 19720, 6084, -33435, -54442, 1547, 115228, 140772, -63880, -372775, -332892, 359763, 1142322, 678796, -1528956, -3323203

Offset

0,4

Comments

The norm of the coefficients in 1/(1 - i*x - i*x^2) is given by A105309.

Links

Paul D. Hanna, Table of n, a(n) for n = 0..500

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

Formula

G.f.: 1/(1 + x^2*(1+x)^2).

a(n) = -(A201838(n-1) + A201838(n-2)), where A201838 gives the imaginary part of the coefficients in 1/(1 - i*x - i*x^2).

a(n) = Re((((i + sqrt(4*i-1))^(n+1) - (i - sqrt(4*i-1))^(n+1)))/(2^(n+1)*sqrt(4*i-1))), where i=sqrt(-1). - Daniel Suteu, Apr 20 2018

a(n) = - a(n-2) - 2*a(n-3) - a(n-4). - Wesley Ivan Hurt, Sep 05 2022

Example

G.f.: A(x) = 1 - x^2 - 2*x^3 + 4*x^5 + 5*x^6 - 2*x^7 - 13*x^8 - 12*x^9 +...
A201838 gives the imaginary part of coefficients in 1/(1 -i*x - i*x^2) and begins: 0, 1, 1, -1, -3, -2, 4, 9, 3, -15, -25, 0, 52, 65, -27, -169, -155, 158, 520,... in which this sequence equals the negative of the pairwise sums of A201838.

Mathematica

Re/@ CoefficientList[Series[1/(1-I*x-I*x^2), {x, 0, 50}], x] (* Harvey P. Dale, Dec 10 2011 *)

Prog

(PARI) {a(n)=real(polcoeff(1/(1-I*x-I*x^2+x*O(x^n)), n))}
(PARI) {a(n)=polcoeff(1/(1 + x^2 + 2*x^3 + x^4 +x*O(x^n)), n)}

Crossrefs

Cf. A201838 (imag), A105309 (norm).

Sequence in context: A258100 A173335 A335118 * A326052 A004482 A329233

Adjacent sequences: A201834 A201835 A201836 * A201838 A201839 A201840

Keyword

sign,easy

Author

Paul D. Hanna, Dec 06 2011

Status

approved