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A211638
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Number of ordered triples (w, x, y) with all terms in {1, ..., n} and w^2 + x^2 + y^2 < n.
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3
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0, 0, 0, 0, 1, 1, 1, 4, 4, 4, 7, 7, 10, 11, 11, 17, 17, 17, 20, 23, 26, 26, 32, 35, 35, 38, 38, 44, 48, 48, 54, 60, 60, 60, 66, 69, 75, 78, 78, 87, 87, 87, 96, 102, 105, 108, 114, 120, 120, 121, 127, 133, 139, 139, 145, 157, 157, 163, 169, 169, 178, 178, 184
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OFFSET
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0,8
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COMMENTS
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For a guide to related sequences, see A211422.
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LINKS
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FORMULA
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MATHEMATICA
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t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w^2 + x^2 + y^2 < n, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 80]] (* A211638 *)
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PROG
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(PARI) first(n) = {n = max(n, 2); n-=2; my(res = vector(n), v = vector(n)); forvec(x = vector(3, i, [1, sqrtint(n)]), c = sum(i = 1, 3, x[i]^2); if(c <= n, v[c]++)); for(i = 2, #v, v[i]+=v[i-1]); concat([0, 0], v)} \\ David A. Corneth, Jun 16 2023
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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