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 A212564 Number of (w,x,y,z) with all terms in {1,...,n} and w+x>2y+2z. 2
 0, 0, 0, 3, 16, 48, 114, 229, 416, 696, 1100, 1655, 2400, 3368, 4606, 6153, 8064, 10384, 13176, 16491, 20400, 24960, 30250, 36333, 43296, 51208, 60164, 70239, 81536, 94136, 108150, 123665, 140800, 159648, 180336, 202963, 227664, 254544, 283746, 315381 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS 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 (3,-1,-5,5,1,-3,1). FORMULA a(n) = 3*a(n-1)-a(n-2)-5*a(n-3)+5*a(n-4)+a(n-5)-3*a(n-6)+a(n-7). From Colin Barker, Dec 05 2015: (Start) a(n) = 1/96*(2*n*(3*((-1)^n-1)+(n-2)*n*(7*n-4))-9*(-1)^n+9). G.f.: x^3*(3+7*x+3*x^2+x^3) / ((1-x)^5*(1+x)^2). (End) MATHEMATICA t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[w + x > 2 y + 2 z, s = s + 1], {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]]; Map[t[#] &, Range[0, 40]]   (* A212564 *) PROG (PARI) concat(vector(3), Vec(x^3*(3+7*x+3*x^2+x^3) / ((1-x)^5*(1+x)^2) + O(x^100))) \\ Colin Barker, Dec 05 2015 CROSSREFS Cf. A211795. Sequence in context: A296947 A255211 A172482 * A222843 A004320 A089363 Adjacent sequences:  A212561 A212562 A212563 * A212565 A212566 A212567 KEYWORD nonn,easy AUTHOR Clark Kimberling, May 21 2012 STATUS approved

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Last modified August 15 13:27 EDT 2020. Contains 336504 sequences. (Running on oeis4.)