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A212570
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Number of (w,x,y,z) with all terms in {1,...,n} and |w-x|=|x-y|+|y-z|.
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7
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0, 1, 6, 23, 52, 105, 178, 287, 424, 609, 830, 1111, 1436, 1833, 2282, 2815, 3408, 4097, 4854, 5719, 6660, 7721, 8866, 10143, 11512, 13025, 14638, 16407, 18284, 20329, 22490, 24831, 27296, 29953, 32742, 35735, 38868, 42217, 45714, 49439
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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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FORMULA
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a(n) = 2a(n-1)+a(n-2)-4a(n-3)+a(n-4)+2a(n-5)-a(n-6).
a(n) = n*(-1-3*(-1)^n+10*n^2)/12. G.f.: x*(x^4+4*x^3+10*x^2+4*x+1)/((x-1)^4*(x+1)^2). [Colin Barker, Oct 04 2012]
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MATHEMATICA
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t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[Abs[w - x] == Abs[x - y] + Abs[y - z], s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 40]] (* A212570 *)
LinearRecurrence[{2, 1, -4, 1, 2, -1}, {0, 1, 6, 23, 52, 105}, 40] (* Harvey P. Dale, Oct 02 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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