A113142 Expansion of x(1-3x+x^2+x^3)/(1+x)^2.

0, 1, -5, 10, -14, 18, -22, 26, -30, 34, -38, 42, -46, 50, -54, 58, -62, 66, -70, 74, -78, 82, -86, 90, -94, 98, -102, 106, -110, 114, -118, 122, -126, 130, -134, 138, -142, 146, -150, 154, -158, 162, -166, 170, -174, 178, -182, 186

Offset: 0

Author

Paul Barry, Oct 15 2005

Keywords

• easy
• sign

Comments

Second column in number triangle A113141.

Links

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

Programs

Mathematica

CoefficientList[Series[(x(1-3x+x^2+x^3))/(1+x)^2,{x,0,100}],x] (* or *) LinearRecurrence[{-2,-1},{0,1,-5,10,-14},100] (* Harvey P. Dale, Mar 23 2021 *)

Formula

a(n) = -(-1)^n*(4n-2-C(1, n-1)+2*C(0, n)).