OFFSET
0,3
LINKS
Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).
FORMULA
a(n) = 5a(n-1)-10a(n-2)+10a(n-3)-5a(n-4)+a(n-5).
G.f.: -x*(1+11*x+10*x^2+x^3) / (x-1)^5.
a(n) = n*(-2+(1+(2+23*n)*n)*n)/24.
MATHEMATICA
t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w < x + y + z, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 50]] (* A212090 *)
FindLinearRecurrence[%]
(* Peter J. C. Moses, Apr 13 2012 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 1, 16, 80, 251}, 34] (* Ray Chandler, Aug 02 2015 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 01 2012
STATUS
approved