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A212521
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Number of (w,x,y,z) with all terms in {1,...,n} and w>=2x and y<=3z.
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2
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0, 0, 4, 18, 60, 138, 297, 528, 912, 1440, 2200, 3180, 4536, 6174, 8330, 10920, 14144, 17928, 22599, 27900, 34300, 41580, 50094, 59664, 70848, 83148, 97344, 113022, 130732, 150150, 172125, 195840, 222464, 251328, 283220, 317628, 355752, 396378, 441142
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OFFSET
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0,3
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COMMENTS
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For a guide to related sequences, see A211795.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,2,2,-1,-4,0,2,0,-2,0,4,1,-2,-2,0,1).
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FORMULA
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a(n) = 2*a(n-2)+2*a(n-3)-a(n-4)-4*a(n-5)+2*a(n-7)-2*a(n-9)+4*a(n-11)+ a(n-12)-2*a(n-13)-2*a(n-14)+a(n-16).
G.f.: x^2*(4 +18*x +52*x^2 +94*x^3 +145*x^4 +166*x^5 +174*x^6 +160*x^7 +133*x^8 +80*x^9 +40*x^10 +12*x^11 +2*x^12) / ((1 -x)^5*(1 +x)^3*(1 -x +x^2)*(1 +x +x^2)^3). - Colin Barker, Dec 11 2015
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MATHEMATICA
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t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w >= 2 x && y <= 3 z, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 50]] (* A212521 *)
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PROG
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(PARI) concat([0, 0], Vec(x^2*(4 +18*x +52*x^2 +94*x^3 +145*x^4 +166*x^5 +174*x^6 +160*x^7 +133*x^8 +80*x^9 +40*x^10 +12*x^11 +2*x^12) / ((1 -x)^5*(1 +x)^3*(1 -x +x^2)*(1 +x +x^2)^3) + O(x^100))) \\ Colin Barker, Dec 11 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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