OFFSET
0,3
COMMENTS
For a guide to related sequences, see A211795.
LINKS
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5).
G.f.: x^2*(4+x)/(1-x)^5. - Bruno Berselli, May 31 2012
a(n) = (n-1)*n*(n+1)*(5*n+6)/24. - Bruno Berselli, May 31 2012
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, 40]] (* A212246 *)
PROG
(PARI) a(n) = n*(n-1)*(n+1)*(5*n+6)/24 \\ Charles R Greathouse IV, Feb 16 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 19 2012
EXTENSIONS
Offset corrected by Charles R Greathouse IV, Feb 16 2015
STATUS
approved