A128019 Expansion of (1 - 3x)/(1 + 3*x^2).

1, -3, -3, 9, 9, -27, -27, 81, 81, -243, -243, 729, 729, -2187, -2187, 6561, 6561, -19683, -19683, 59049, 59049, -177147, -177147, 531441, 531441, -1594323, -1594323, 4782969, 4782969, -14348907, -14348907, 43046721, 43046721, -129140163, -129140163, 387420489, 387420489

Offset: 0

Author

Paul Barry, Feb 11 2007

Keywords

• easy
• sign

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,-3)

Crossrefs

Cf. A108411, A128018.

Programs

Mathematica

CoefficientList[Series[(1 - 3x)/(1 + 3*x^2),{x,0,40}],x] (* Stefano Spezia, Dec 31 2022 *)
LinearRecurrence[{0,-3},{1,-3},40] (* Harvey P. Dale, Jun 09 2025 *)

Formula

a(n) = 3^floor((n+1)/2)*(-1)^C(n+1,2).

Binomial transform is A128018.

E.g.f.: cos(sqrt(3)*x) - sqrt(3)*sin(sqrt(3)*x). - Stefano Spezia, Dec 31 2022