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A213501
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Number of (w,x,y) with all terms in {0,...,n} and w != max(|w-x|,|x-y|)
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2
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0, 4, 16, 45, 94, 172, 281, 433, 626, 875, 1177, 1547, 1981, 2497, 3087, 3772, 4543, 5421, 6396, 7492, 8695, 10032, 11488, 13090, 14822, 16714, 18746, 20951, 23308, 25850, 28555, 31459, 34536, 37825, 41299, 44997, 48891, 53023, 57361, 61950, 66757, 71827
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OFFSET
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0,2
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COMMENTS
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For a guide to related sequences, see A212959.
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LINKS
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FORMULA
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a(n) = a(n-1)+2*a(n-2)-a(n-3)-2*a(n-4)-a(n-5)+2*a(n-6)+a(n-7)-a(n-8).
G.f.: x*(4 + 12*x + 21*x^2 + 21*x^3 + 12*x^4 + 2*x^5))/((1 - x)^4*(1 + x)^2*(1 + x + x^2)).
a(n) = (6*n*(n+1)*(24*n+17)-9*(2*n+1)*(-1)^n+32*cos(2*pi*(n+2)/3)+25)/144. - Bruno Berselli, Jul 02 2012
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MATHEMATICA
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t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w != Max[Abs[w - x], Abs[x - y]], s = s + 1],
{w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];
m = Map[t[#] &, Range[0, 60]] (* A213501 *)
LinearRecurrence[{1, 2, -1, -2, -1, 2, 1, -1}, {0, 4, 16, 45, 94, 172, 281, 433}, 50] (* Harvey P. Dale, Oct 01 2021 *)
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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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