A168058 Expansion of x + sqrt(1-2x-3x^2).

1, 0, -2, -2, -4, -8, -18, -42, -102, -254, -646, -1670, -4376, -11596, -31022, -83670, -227268, -621144, -1706934, -4713558, -13072764, -36398568, -101704038, -285095118, -801526446, -2259520830, -6385455594, -18086805002

Offset: 0

Author

Paul Barry, Nov 17 2009

Keywords

• easy
• sign

Comments

a(n+2) = -2*A001006(n). Hankel transform is (-1)^n*A168057(n).

Essentially the same as A167022. - R. J. Mathar, Nov 18 2009

Examples

			1 - 2*x^2 - 2*x^3 - 4*x^4 - 8*x^5 - 18*x^6 - 42*x^7 - 102*x^8 - 254*x^9 - ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A168055.

Programs

Mathematica

CoefficientList[Series[x + Sqrt[1 - 2 x - 3 x^2], {x, 0, 50}], x] (* G. C. Greubel, Jul 08 2016 *)

Formula

a(n) = 0^n - 2*Sum_{k=0..floor((n-2)/2)} C(n-2,2k)*A000108(k).

D-finite with recurrence: n*a(n) +(-2*n+3)*a(n-1) +3*(-n+3)*a(n-2)=0. - R. J. Mathar, Jan 23 2020