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 A054221 Consider all integer triples (i,j,k), j,k>0, with binomial(i+2,3)=binomial(j+2,3)+k^3, ordered by increasing i; sequence gives i values. 4
 7, 8, 10, 23, 27, 48, 64, 125, 199, 216, 343, 512, 621, 729, 978, 1000, 1222, 1331, 1728, 2197, 2744, 3375, 3563, 4034, 4096, 4331, 4913, 5017, 5832, 6442, 6859, 6886, 7783, 8000, 8699, 9261, 10648, 11157, 12167, 12287, 12386, 13824, 15625, 17576, 19683 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Sequence contains all positive cubes, since binomial(n+2,3)-binomial(n,3)=n^2. j values are A054222 and k values are A054223. LINKS Bert Dobbelaere, Table of n, a(n) for n = 0..271 (terms 0..84 from Joerg Arndt) EXAMPLE binomial(7+2,3)=84=binomial(4+2,3)+4^3; binomial(8+2,3)=120=binomial(6+2,3)+4^3; MATHEMATICA max = 20000; s = {}; Do[k = ((i*(i+1)*(i+2) - j*(j+1)*(j+2))/6)^(1/3); If[IntegerQ[k], Print[i]; AppendTo[s, i]], {j, 1, max}, {i, j+1, max}]; Sort[s] (* Jean-François Alcover, Oct 12 2011 *) PROG (C) #include #include #include typedef unsigned long long ULL; unsigned A000578inv(ULL n) { ULL n3 = (ULL)cbrt((double)n) ; for (ULL k= n3-1 ; k <= n3+1 ; k++) if ( k*k*k == n) return k; return 0 ; } int main(int argc, char *argv[]) { const ULL imax = cbrt((double)ULLONG_MAX)-2. ; for(unsigned i=1; i0: ....if delta>0: ......kd3+=6; kd2+=kd3; delta-=kd2; k+=1; ....else: ......if delta==0: ........print("A054221(%d)= %d, A054222(%d)= %d, A054223(%d)= %d"% ..............(n, i, n, j, n, k)); n+=1; ......delta += T_j; T_j-=j; j-=1; # Bert Dobbelaere, Jan 14 2019 CROSSREFS Cf. A054222, A054223. Sequence in context: A286420 A111064 A071117 * A195240 A253318 A277026 Adjacent sequences: A054218 A054219 A054220 * A054222 A054223 A054224 KEYWORD nice,nonn AUTHOR Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Feb 04 2000 EXTENSIONS More terms from R. J. Mathar, Nov 10 2006 STATUS approved

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Last modified June 14 12:19 EDT 2024. Contains 373400 sequences. (Running on oeis4.)