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 A212134 Number of (w,x,y,z) with all terms in {1,...,n} and median<=mean. 3
 0, 1, 12, 57, 172, 405, 816, 1477, 2472, 3897, 5860, 8481, 11892, 16237, 21672, 28365, 36496, 46257, 57852, 71497, 87420, 105861, 127072, 151317, 178872, 210025, 245076, 284337, 328132, 376797, 430680, 490141, 555552, 627297, 705772, 791385, 884556, 985717 (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..1000 Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA a(n)+ A212135(n) = n^4. a(n) = n*(n^3 + 2*n^2 - 3*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.: x*(1 + 7*x + 7*x^2 - 3*x^3) /(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, 50]]] (* A212134 *) (* Peter J. C. Moses, May 01 2012 *) PROG (PARI) concat(0, Vec(x*(1 + 7*x + 7*x^2 - 3*x^3) /(1 - x)^5 + O(x^40))) \\ Colin Barker, Dec 02 2017 CROSSREFS Cf. A211795, A212133. Sequence in context: A204674 A123983 A212682 * A071270 A051877 A212065 Adjacent sequences: A212131 A212132 A212133 * A212135 A212136 A212137 KEYWORD nonn,easy AUTHOR Clark Kimberling, May 04 2012 STATUS approved

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Last modified March 4 12:45 EST 2024. Contains 370532 sequences. (Running on oeis4.)