A212246 Number of (w,x,y,z) with all terms in {1,...,n} and w <= x > y <= z.

0, 0, 4, 21, 65, 155, 315, 574, 966, 1530, 2310, 3355, 4719, 6461, 8645, 11340, 14620, 18564, 23256, 28785, 35245, 42735, 51359, 61226, 72450, 85150, 99450, 115479, 133371, 153265, 175305, 199640, 226424, 255816, 287980, 323085

Offset: 0

Author

Clark Kimberling, May 19 2012

Keywords

• nonn
• easy

Comments

For a guide to related sequences, see A211795.

Links

• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A211795.

Programs

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 *)

PARI

a(n) = n*(n-1)*(n+1)*(5*n+6)/24 \\ Charles R Greathouse IV, Feb 16 2015

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

Extensions

Offset corrected by Charles R Greathouse IV, Feb 16 2015