A058923 a(n) = binomial(n,0) - binomial(n,2) + binomial(n,4).

1, 1, 0, -2, -4, -4, 1, 15, 43, 91, 166, 276, 430, 638, 911, 1261, 1701, 2245, 2908, 3706, 4656, 5776, 7085, 8603, 10351, 12351, 14626, 17200, 20098, 23346, 26971, 31001, 35465, 40393, 45816, 51766, 58276, 65380, 73113, 81511, 90611, 100451, 111070, 122508

Offset: 0

Author

N. J. A. Sloane, Jan 12 2001

Keywords

• sign
• easy

Links

• Harry J. Smith, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A000127.

Programs

Mathematica

CoefficientList[Series[-((z - 1)*z*((z - 1)*z + 4) + 1)/(z - 1)^5, {z, 0, 100}], z] (* Vladimir Joseph Stephan Orlovsky, Jul 16 2011 *)
Table[Binomial[n,0]-Binomial[n,2]+Binomial[n,4],{n,0,50}] (* or *) LinearRecurrence[{5,-10,10,-5,1},{1,1,0,-2,-4},50] (* Harvey P. Dale, Mar 02 2015 *)

PARI

a(n) = 1 - binomial(n,2) + binomial(n,4) \\ Harry J. Smith, Jun 24 2009

PARI

Vec(-(1-4*x-2*x^3+x^4+5*x^2)/(x-1)^5 + O(x^60)) \\ Michel Marcus, Jan 03 2016

Formula

From R. J. Mathar, Mar 17 2009: (Start)

a(n) = 5a(n-1)-10a(n-2)+10a(n-3)-5a(n-4)+a(n-5).

G.f.: -(1-4*x-2*x^3+x^4+5*x^2)/(x-1)^5. (End)