A212135 Number of (w,x,y,z) with all terms in {1,...,n} and median<mean.

0, 0, 4, 24, 84, 220, 480, 924, 1624, 2664, 4140, 6160, 8844, 12324, 16744, 22260, 29040, 37264, 47124, 58824, 72580, 88620, 107184, 128524, 152904, 180600, 211900, 247104, 286524, 330484, 379320, 433380, 493024, 558624, 630564, 709240, 795060, 888444

Offset

0,3

Comments

Also, the number of (w,x,y,z) with all terms in {1,...,n} and median>mean.

For a guide to related sequences, see A211795.

Links

Colin Barker, Table of n, a(n) for n = 0..1001

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

Formula

a(n) + A212134(n) = n^4.

a(n) = n*(n - 1)*(n^2 - n + 2)/2.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).

G.f.: 4*x*(1 + x + x^2) / (1 - x)^5. - Colin Barker, Dec 02 2017

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[
Apply[Plus, Rest[Most[Sort[{w, x, y, z}]]]]/2 > (w + x + y + z)/4, s = s + 1], {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Flatten[Map[{t[#]} &, Range[0, 20]]]  (* A212135 *)
%/4 (* A002817 *)

Prog

(PARI) concat(vector(2), Vec(4*x*(1 + x + x^2) / (1 - x)^5 + O(x^40))) \\ Colin Barker, Dec 02 2017

Crossrefs

Cf. A211795.

Sequence in context: A264184 A354476 A211071 * A210569 A334581 A341688

Adjacent sequences: A212132 A212133 A212134 * A212136 A212137 A212138

Keyword

nonn,easy

Author

Clark Kimberling, May 05 2012

Status

approved