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 A212565 Number of (w,x,y,z) with all terms in {1,...,n} and w+x>=2y+2z. 2
 0, 0, 1, 8, 28, 74, 159, 304, 528, 860, 1325, 1960, 2796, 3878, 5243, 6944, 9024, 11544, 14553, 18120, 22300, 27170, 32791, 39248, 46608, 54964, 64389, 74984, 86828, 100030, 114675, 130880, 148736, 168368, 189873, 213384, 239004, 266874, 297103, 329840 (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*(14*n^4-12*n^3-8*n^2-6*((-1)^n-1)*n+3*((-1)^n-1)). G.f.: x^2*(1+5*x+5*x^2+3*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]]   (* A212565 *) PROG (PARI) concat([0, 0], Vec(x^2*(1+5*x+5*x^2+3*x^3)/((1-x)^5*(1+x)^2) + O(x^100))) \\ Colin Barker, Dec 05 2015 CROSSREFS Cf. A211795. Sequence in context: A153976 A105636 A102665 * A209408 A316214 A134638 Adjacent sequences:  A212562 A212563 A212564 * A212566 A212567 A212568 KEYWORD nonn,easy AUTHOR Clark Kimberling, May 21 2012 STATUS approved

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Last modified August 8 14:36 EDT 2020. Contains 336298 sequences. (Running on oeis4.)