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 A212135 Number of (w,x,y,z) with all terms in {1,...,n} and median
 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 (list; graph; refs; listen; history; text; internal format)
 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: A069145 A264184 A211071 * A210569 A005561 A061612 Adjacent sequences:  A212132 A212133 A212134 * A212136 A212137 A212138 KEYWORD nonn,easy AUTHOR Clark Kimberling, May 05 2012 STATUS approved

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Last modified February 22 08:42 EST 2020. Contains 332133 sequences. (Running on oeis4.)