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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

For a guide to related sequences, see A211795.

LINKS

Table of n, a(n) for n=0..35.

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

Cf. A211795.

Sequence in context: A254449 A131478 A089893 * A095668 A078800 A184706

Adjacent sequences:  A212243 A212244 A212245 * A212247 A212248 A212249

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 19 2012

EXTENSIONS

Offset corrected by Charles R Greathouse IV, Feb 16 2015

STATUS

approved

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Last modified June 14 10:04 EDT 2021. Contains 345025 sequences. (Running on oeis4.)