OFFSET
0,4
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).
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)
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 *)
PROG
(PARI) for (n = 0, 200, write("b058923.txt", 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
CROSSREFS
KEYWORD
sign,easy
AUTHOR
N. J. A. Sloane, Jan 12 2001
STATUS
approved