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 A212098 Number of (w,x,y,z) with all terms in {1,...,n} and w^3<=x^3+y^3+z^3. 3
 0, 1, 15, 72, 221, 536, 1104, 2034, 3451, 5514, 8380, 12246, 17322, 23812, 31981, 42107, 54457, 69350, 87100, 108049, 132591, 161085, 193966, 231592, 274511, 323077, 377830, 439314, 507948, 584401, 669124, 762764, 865882, 979130 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n)+A212099(n)=n^4. For a guide to related sequences, see A211795. LINKS Giovanni Resta, Table of n, a(n) for n = 0..1000 MAPLE f:= proc(n) local x, y, z, r, t; r:= 0: for x from 1 to n do for y from x to n do for z from y to n do t:= min(n, floor((x^3 + y^3 + z^3)^(1/3))); if x = z then r:= r+t elif x=y or y=z then r:= r+3*t else r:= r+6*t fi od od od; r end proc: map(f, [\$0..40]); # Robert Israel, May 08 2017 MATHEMATICA t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[w^3 <= x^3 + y^3 + z^3, s = s + 1], {w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]]; Map[t[#] &, Range[0, 40]] (* A212098 *) (* Peter J. C. Moses, Apr 13 2012 *) PROG (PARI) A212098(n)={my(s=0, c=[6, 3, 1]); forvec(v=vector(4, i, if(i>1, [1, n], [-n, -1])), sum(i=1, 4, v[i]^3)>=0&s+=c[1+(v[2]==v[3])+(v[3]==v[4])], 1); s} /* not very efficient */ M. F. Hasler, May 20 2012 CROSSREFS Cf. A211795, A212099. Sequence in context: A126274 A241234 A212097 * A053531 A000476 A002603 Adjacent sequences: A212095 A212096 A212097 * A212099 A212100 A212101 KEYWORD nonn AUTHOR Clark Kimberling, May 03 2012 STATUS approved

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Last modified May 25 04:20 EDT 2024. Contains 372782 sequences. (Running on oeis4.)