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A245621 Sequence of distinct least nonnegative numbers such that the average of the first n terms is a cube. 1

%I

%S 0,2,1,29,8,122,27,323,64,674,125,1217,216,1994,343,3047,512,4418,729,

%T 6149,1000,8282,1331,10859,1728,13922,2197,17513,2744,21674,3375,

%U 26447,4096,31874,4913,37997,5832,44858,6859,52499,8000,60962,9261,70289,10648,80522,12167,91703,13824

%N Sequence of distinct least nonnegative numbers such that the average of the first n terms is a cube.

%F Conjecture: a(2*n+1) = n^3, a(2*n) = 7*n^3 - 9*n^2 + 5*n - 1.

%F Conjecture: a(n) = 4*a(n-2)-6*a(n-4)+4*a(n-6)-a(n-8) for n>8. - _Colin Barker_, Nov 05 2014

%F Empirical g.f.: x^2*(x^6+x^5+18*x^4+4*x^3+21*x^2+x+2) / ((x-1)^4*(x+1)^4). - _Colin Barker_, Nov 05 2014

%o (PARI) v=[]; n=0; while(n<50000, num=(vecsum(v)+n); if(num%(#v+1)==0&&vecsearch(vecsort(v), n)==0, for(i=0, n, if(i^3>(num/(#v+1)), break); if(i^3==(num/(#v+1)), print1(n, ", "); v=concat(v, n); n=0; break))); n++)

%Y Cf. A245624, A245625.

%K nonn

%O 1,2

%A _Derek Orr_, Nov 05 2014

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Last modified May 25 15:54 EDT 2022. Contains 354071 sequences. (Running on oeis4.)