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A212246
Number of (w,x,y,z) with all terms in {1,...,n} and w <= x > y <= z.
4
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
0,3
COMMENTS
For a guide to related sequences, see A211795.
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
Cf. A211795.
Sequence in context: A254449 A131478 A089893 * A359065 A095668 A078800
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 19 2012
EXTENSIONS
Offset corrected by Charles R Greathouse IV, Feb 16 2015
STATUS
approved