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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
OFFSET
0,4
COMMENTS
For a guide to related sequences, see A211795.
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 21 2012
STATUS
approved